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PLATE  I 


PRIMARY  COLORS, 


FORBES  CO  ..BOSTON. 


THE 


ELEMENTS    OE   PHYSICS 


A  TEXT-BOOK  FOR  HIGH   SCHOOLS 
AND   ACADEMIES 


BY 


ALFRED   PAYSON   GAGE,  PH.D. 

AUTHOR,  OF  "PRINCIPLES  OF  PHYSICS,"   "INTRODUCTION  TO 

PHYSICAL  SCIENCE,"  ETC. 


REVISED   EDITION 


f   UNIVERSITY    1 

\       OF      / 


BOSTON,  U.S.A. 

GINN   &   COMPANY,   PUBLISHERS 
at&enaettm 

1898 


( 


COPYRIGHT,  1882 
BY  ALFRED  PAYSON  GAGE 


COPYRIGHT,  1898 
BY   ALFRED  PAYSON  GAGE 


ALT,,  RIGHTS   KKSKKVED 


PREFACE. 


SEVENTEEN  years  ago,  in  the  preface  to  the  first  edition  of 
this  work,  the  author  urged  the  importance  of  experiments  to 
be  performed  by  the  pupil,  as  an  aid  to  his  mastery  of  the 
science  of  Physics,  in  opposition  to  the  then  universal  and 
exclusive  text-book-memorizing  or  illustrated-lecture  system. 
In  these  seventeen  years  he  has  seen  the  value  of  the  "  objec- 
tive method  of  study  "  demonstrated  in  the  case  of  more  than 
two  thousand  pupils  in  his  own  classes,  and  has  witnessed 
the  spread  of  the  "  laboratory  method  "  of  teaching  science 
through  the  larger  portion  of  the  high  schools  of  the  United 
States.  But  with  this  great  improvement  in  educational 
method,  he  has  observed  the  development  of  a  tendency 
which  threatens  seriously  to  impair  its  usefulness. 

This  is  the  tendency  to  allow  enthusiasm  for  experimen- 
tation, for  mere  manipulation  of  apparatus,  to  obscure  the 
importance  of  an  intellectual  mastery  of  the  facts  and  their 
underlying  principles.  In  their  zeal  for  "  training  the  mental 
powers  "  of  their  pupils,  teachers  may  easily  reduce  the  study 
of  physical  science  to  a  mere  gymnastic,  forgetting  that  the 
object  of  training  the  mind  is  to  render  possible  the  greater 
acquisition  of  knowledge.  If,  then,  the  pupil  has  not  at  the 
end  of  his  course  a  reasonably  comprehensive  and  accurate 
grasp  of  the  subject-matter  of  Physics,  the  instructor  may  be 
sure  that  he  has  failed  to  preserve  a  due  proportion  between 
study  and  experiment. 

The  author  is  convinced  that  both  mental  discipline  and 
the  acquisition  of  knowledge  will  be  promoted  if  theory  and 

96804 


IV  PREFACE. 

experiment  be  somewhat  sharply  divided.  If  on  the  same 
page  the  pupil  reads  a  statement  of  a  scientific  principle,  the 
facts  on  which  it  is  based,  the  reasoning  by  which  it  is 
deduced,  together  with  elaborate  detailed  directions  for  pre- 
paring apparatus  for  exhibiting  the  facts  in  a  series  of  experi- 
ments, and  minute  directions  for  the  manipulation,  he  is 
almost  certain  to  fail  to  discriminate  in  regard  to  the  relative 
importance  of  each  of  these  matters,  and  the  relation  which 
each  sustains  to  the  purposes  of  his  study ;  he  is  likely  to 
bestow  equal  attention  upon  each  —  even  (if  not  wholly 
emancipated  from  childish  methods)  to  memorize  all  alike. 
To  obviate  the  danger  of  this  enormous  misdirection  of  effort, 
the  author  has  been  led  to  construct  a  separate  Manual  of 
"  Physical  Experiments,"  by  the  use  of  which  the  attention  of 
the  pupil  is  concentrated  upon  apparatus,  process,  result,  and 
inference,  and  to  treat  matter  in  the  text-book  principally  as 
a  body  of  systematized  knowledge  to  be  mastered  —  a  science 
in  the  strictest  application  of  that  term. 

In  the  laboratory,  then,  the  pupil  should  do,  should  observe, 
should  reflect,  should  infer,  and  should  record  the  results  of 
these  processes  in  a  suitable  manner.  In  the  class-room  he 
should  concentrate  his  attention  upon  the  theory  and  principles 
of  the  science  as  laid  down  in  the  text-book,  striving  to  bring 
these  and  the  results  recorded  in  his  manual  into  their  proper 
relations  in  his  mind  as  a  portion  of  a  unified  whole,  the 
possession  of  which  shall  make  him  master  of  one  department 
of  human  knowledge. 

Certain  topics  that  come  under  the  head  of  molecular 
physics,  e.g.  absorption,  osmosis,  and  crystallization,  have 
been  omitted  in  this  revision,  since  their  processes  are  deemed 
too  obscure  and  imperfectly  understood  to  be  classified  under 
the  title  of  scientific  knowledge.  That  department  of  ether 
dynamics  known  as  double  refraction  and  polarization  of 
light  has  been  omitted,  as  it  is  generally  conceded  to  be  too 
difficult  of  apprehension  for  the  average  high-school  pupil. 


PREFACE.  v 

The  author  wishes  to  make  special  acknowledgments  for 
valuable  suggestions  and  aid  in  correcting  the  proofs  to  his 
friend,  Dr.  Arthur  W.  Goodspeed,  of  the  University  of  Penn- 
sylvania, and  to  Mr.  Albert  P.  Walker,  his  colleague  in  the 
English  High  School,  Boston,  who  has  read  the  work  in  manu- 
script and  in  proof  sheets. 


COSTEJSTTS. 


CHAPTER  I. 

Introduction. 

PAGES 

Domain  of  Physics.  Some  properties  of  matter.  Physical  measure- 
ments. Kinematics.  Laws  of  accelerated  motion.  Composition 
of  motions  and  velocities.  Kinds  of  motion 1-24 


CHAPTER  II. 
Molar  Dynamics. 

Force.  Newton's  Laws  of  Motion.  Momentum.  Measurement  of 
force.  Composition  of  forces.  Moments  of  force.  Center  of  mass. 
Curvilinear  motion.  The  pendulum.  Gravitation.  Work,  energy, 
and  power.  Machines.  Properties  of  matter  due  to  molecular 
forces 25-97 

CHAPTER  III. 
Dynamics  of  Fluids. 

Law  of  transmission  of  pressure.  Pascal's  Principle.  Atmospheric 
pressure.  Boyle's  Law.  Barometer.  Principle  of  Archimedes. 
Specific  gravity 98-123 

CHAPTER  IV. 

Molecular  Dynamics.     Heat. 

Theory  of  heat.  Sources  of  heat.  Thermometry.  Calorimetry. 
Specific  heat.  Laws  of  gaseous  bodies.  Fusion.  Latent  heat. 
Artificial  cold.  Hygrometry.  Diffusion  of  heat.  Thermo-dynamics. 
Steam  engine  ..,,.,,., 124-165 


viii  CONTENTS. 

CHAPTER  V. 

Energy  of  Mass  Vibration. 

PAGES 

Simple  harmonic  motion.  Wave-motion.  Sound-waves.  Reenforce- 
ment  of  sound-waves.  Pitch.  Composition  of  wave-forms.  Dis- 
cord and  harmony.  Musical  instruments.  Vocal  organs.  The 
ear 166-205 

CHAPTER  VI. 
Ether  Dynamics.    Radiant  Energy. 

The  ether.  Radiation.  Light.  Intensity  of  illumination.  Mirrors. 
Refraction.  Prisms  and  lenses.  Prismatic  analysis  of  light. 
Spectroscopy.  Color.  Optical  instruments.  The  eye.  Thermal 
effects  of  radiation .  206-267 

CHAPTER  VII. 

Ether  Dynamics.    Electrostatics. 

Electrification.     Conduction.     Induction.     Potential.     Atmospheric 

electricity 268-278 

CHAPTER  VIII. 

Electrokinetics. 

Voltaic  cells.  Effects  producible  by  electric  current.  Electrical 
quantities.  Ohm's  law.  Instruments  for  measurement  of  electric 
current.  Resistance  and  its  measurement.  Divided  circuits. 
Methods  of  combining  cells.  Magnets  and  magnetism.  Magnetic 
relations  of  the  current.  Mutual  action  of  currents.  Electro- 
magnetic induction.  Dynamos.  Electric  motors.  Storage  bat- 
teries. Thermo-electric  currents.  Electric  light.  Electroplating 
and  electrotyping.  Telegraph.  Telephone  and  microphone. 
Electro-magnetic  theory  of  light.  Radiography.  Tesla's  inves- 
tigations   279-365 

Appendix 367-375 

Index 377-381 


LIST    OF    PLATES    AND    PORTRAITS. 


PAGE 

SPECTRUMS,  PLATE  I     ....  ,  Frontispiece. 

SIR  ISAAC  NEWTON 28 

GALILEO           ....                         38 

ARCHIMEDES .  118 

BENJAMIN  FRANKLIN     ..........  278 

LORD  KELVIN ...  306 

MICHAEL  FARADAY        ..........  330 

TELEGRAPH,  PLATE  II 355 

RADIOGRAPH,  PLATE  III       ...                .....  362 


Read  Nature 


. 

f  Experiment. 


ELEMENTS    OF    PHYSICS. 


CHAPTER   I. 
INTRODUCTION. 


SECTION  I. 

DOMAIN    OF   PHYSICS. 

1.  The  perception  of  changes  constantly  taking  place  in  the 
external  world  is  a  universal  human  experience.     The  mani- 
festations of  these  changes  to  the  senses  are  called  phenomena; 
that  which  undergoes  change  is  called  matter.      Since  most  of 
the  changes  which  come  within  the  scope  of  our  present  study 
are  due  to  the  motions 1  of  portions  of  matter,  we  may  adopt 
the  following  provisional  definition:2 

Physics  is  the  science  which  treats  of  the  phenomena  of 
matter  and  motion. 

2,  Some  Properties  of  Matter  or  of  Material  Bodies: 

(1)  Extension.  Every  portion  of  matter,  however  small, 
occupies  space,  i.e.  it  has  length,  breadth,  and  thickness.  The 
property  thus  manifested  is  called  extension. 

1  Sound,  heat,  and  light,  considered  as  distinct  from  the  sensations  to  which  they 
give  rise,  are  nothing  but  motions. 

"  I  do  not  believe  that  there  exists  in  external  bodies  anything  for  exciting  tastes, 
smells,  and  sounds,  but  motion,  swift  or  slow  ;  and  if  tongues,  noses,  and  ears  were 
removed,  I  am  of  the  opinion  that  motion  would  remain,  but  there  would  be  an  end 
of  tastes,  smells,  and  sounds."  —  GALTLEO. 

2  A  provisional  definition  is  one  that  answers  present  needs. 


2  INTRODUCTION. 

(2)  Impenetrability.    While  matter  occupies  any  portion  of 
space  it  excludes  all  other  matter  from  that  portion.     It  is  an 
axiom,  exemplified  in  everyday  experience,  that  no  two  bodies 
(e.g.  our  two  hands)  can  occupy  the  same  space  at  the  same 
time.1     The  property  in  virtue  of  which  a  body  occupies  space 
to  the  exclusion  of  all  other  bodies  is  called  impenetrability. 

Air  and  other  gases  are  invisible,  and  hence  are  not  readily  recognized 
as  matter.  If,  however,  we  show  that  air 
possesses  impenetrability,  we  have  reason  to 
believe  that  air  is  matter,  since  it  possesses 
one  of  the  characteristic  properties  of 
matter. 

Experiment  1.  —  Float  a  cork  on  a  sur- 
face of  water,  cover  it  with  a  tumbler  as  in 
Fig.  1,  and  force  the  tumbler,  mouth  down- 
ward,  deep  into  the  water.     State  what 
evidence  the  experiment  furnishes  that  air  is  matter. 

(3)  Divisibility.      Bodies    of   matter   with   which  we   are 
acquainted  are  divisible  beyond  any  appreciable  limits,  but 
scientists  assume  that  there  are  ultimate  portions  which  can- 
not undergo  further  division.     It  is  certain  that  every  kind 
of  material  substance  known  has  a  minimum  limit  of  division 
which  is  never  exceeded  in  that  substance.     A  molecule  of  any 
substance  is  one  of  the  ultimate  homogeneous  portions  of  which 
the  substance  is  composed. 

A  grain  of  musk  will  scent  a  room  for  years  by  constantly  discharging 
into  the  air  particles  of  musk.  These  particles  are  so  small  that  the 
original  grain  does  not  perceptibly  diminish  in  weight.  Yet  the  smallest 
particle  of  musk  dust,  or  the  smallest  particle  of  any  substance  that  can 
be  obtained  by  mechanical  division,  is  very  large  in  comparison  with  the 
molecules  of  which  the  particle  is  composed.2 

1  This  is  quite  as  axiomatic  as  the  fact  that  "  a  body  cannot  be  in  two  places  at 
the  same  time." 

2  "  In  a  cubic  inch  of  any  gas  at  atmospheric  pressure  and  at  ordinary  tempera- 
tures there  are  about  3  x  1020  detached  particles  absolutely  similar  and  equal  to  one 
another."  —  TAIT. 


PROPERTIES    OF    MATTER.  3 

(4)  Compressibility  and  expansibility.  All  bodies  of  matter 
are  compressible  and  expansible,  though  in  very  different 
degrees.  A  proof  of  the  existence  of  molecules  and  the 
molecular  constitution  of  bodies  (though  by  no  means  the 
most  conclusive  proof)  may  be  found  in  this  fact.  Matter 
(e.g.  gold  or  water)  is  either  continuous  as  it  appears  to  the  eye, 
or  it  is  discontinuous,  granular,  composed  of  distinct  particles 
(molecules)  somewhat  as  represented  in  Fig.  2. 
But  bodies  are  compressible  and  expansible.  •'.'•': '.:•.'•• 

On  the  supposition  that  matter  is  continu-  EXPANDED  :'..'•'•'•'.":'•••' 

STATE       ..     •     '  *  '    .*.'.'.* 

ous,  these  phenomena  are  unexplainable  ;  but  .'.'•'.  •. '.; '. : '.; • 

on  the  supposition  that  matter  is  granular  '\..'.'.  :.'.:./*'• 

or   molecular   they   are    easily   explainable.    CON!TATEED£@£ 
According  to  the  latter  supposition,  a  change 
of  volume  by  contraction  or  expansion  means 
simply  a  coming  together  or  a  separation  of  the  molecules  com- 
posing the  body,  as  represented  in  Fig.  2. 

3.    Theory  of  the  Constitution  of  Matter.    Porosity.  —  For 

reasons  which  will  appear  as  our  knowledge  of  matter  is 
extended,  physicists  have  generally  adopted  the  following 
theory  of  the  constitution  of  matter  :  Every  body  of  matter  except 
the  molecule  is  composed  of  exceedingly  small  disconnected  parti- 
cles, called  molecules.  No  two  molecules  of  matter  in  the  universe 
are  in  permanent  contact  with  each  other.  Every  molecule  is 
in  rapid  motion,  moving  back  and  forth  among  its  neighbors, 
hitting  and  rebounding  from  them.  When  we  heat  a  body  we 
simply  cause  the  molecules  to  move  more  rapidly  through  their 
spaces,  so  they  strike  harder  blows  on  their  neighbors,  and 
usually  push  them  away  a  very  little  ;  hence  the  body  expands. 
If  the  molecules  of  a  body  are  never  in  contact  except  at 
the  instants  of  collision,  it  follows  that  there  are  spaces  between 
them.  These  spaces  are  called  pores. 

It  is  estimated  that  even  in  dense  solids  the  average  distance  between 
molecules  is  many  times  the  diameter  of  a  molecule, 


4  INTRODUCTION. 

-  All  matter  is  porous  ;  thus  water  may  be  forced  through  the  pores  of 
cast  iron;  and  gold,  one  of  the  densest  of  substances,  absorbs  liquid 
mercury. 

Impenetrability  may  be  affirmed  of  molecules,  but  not  necessarily  of 
masses.  The  term  pores,  in  physics,  is  restricted  to  the  invisible  spaces 
that  separate  molecules,  and  does  not  include  such  cavities  as  may  be  seen 
with  the  naked  eye,in  sponges,  and  with  a  microscope  in  wood,  etc. 

4,  Physical   Measurements.  —  Physics    is    essentially    a 
science   of    measurements.      Measuring   consists    in   finding 
how  many  times  a  definite  quantity,  called  a  unit,  is  con- 
tained in  the  quantity  to  be  measured.     For  example,  should 
we  wish  to  measure  the  length  of  a  table,  we  may  choose 
arbitrarily  for  a  unit  of  measurement  the  length  of  a  certain 
pencil  and  proceed  to  find  how  many  times  this  pencil  may 
be  laid  along  the  length  of  the  table.     If  ten  times,  we  say 
the  table  is  ten  pencil-lengths  long. 

The  unit  of  measurement  must  be  a  definite  quantify  of  the 
same  kind  as  the  thing  to  be  measured.  Thus  a  unit  for  meas- 
uring length  must  be  a  certain  length,  a  unit  for  measuring 
surface  ^nust  be  a  certain  quantity  of  surface,  and  a  unit  for 
measuring  volume  must  be  a  definite  volume.  A  unit  which 
has  become  legalized  either  by  statute  or  by  common  usage  is 
called  a  standard  unit.  The  expression  of  a  physical  quantity 
consists  of  a  statement  of  the  concrete  unit  employed,  e.g. 
pound,  foot,  quart,  etc.,  with  the  number  of  those  units  pre- 
fixed. The  numerical  part,  called  the  numeric,  is  obtained 
by  measurement. 

5,  Metric  System  of  Measures.  —  [In  this  connection  the 
Tables    of   Metric   Measures,    in   the   Appendix,   should    be 
studied.]     The  term  metric  is  derived  from  the  word  meter, 
which  is  the  name  of  the  fundamental  unit  employed  in  this 
system  for  measuring  length.      The  international  standard 
meter  is  defined  by  law  to  be  the  shortest  distance  between 
two  lines  engraved  on  a  given  platinum  bar  (carefully  pre- 
served by  the   French   government)  at  the   temperature   of 


VOLUME,    MASS,    DENSITY.  5 

0°  C.  (32°  F.).1    The  metric  system  is  now  generally  employed 
in  scientific  work.2 

6.  Volume,  Mass,  and  Density. — The  quantity  of  space  a 
body  of  matter  occupies  is  its  volume,  and  is  expressed  in 
cubic  inches,  cubic  centimeters,  etc.  By  the  mass  of  a  body 
is  meant  the  quantity  of  matter  in  the  body. 

The  unit  of  mass  generally  employed  in  science  is  the  gram, 
or,  in  the  British  system,  the  pound.  The  gram  is  the  one- 
thousandth  part  of  the  standard  kilogram.  This  standard  is 
a  piece  of  platinum  carefully  preserved  by  the  French  gov- 
ernment at  Paris.  Originally  it  was  intended  to  represent 
the  mass  of  a  cubic  decimeter  of  pure  water  at  the  tempera- 
ture of  4°  C.  A  kilogram  of  any  substance  is  that  quantity  of 
the  substance  which,  placed  on  a  scale  pan,  would  just  balance 
in  a  vacuum  the  standard  kilogram  placed  on  the  other  pan. 


Experiment  2.  —  Place  on  one  pan  of  a  balance  (Fig.  3)  a  vessel,  A, 
whose  capacity  is  one  liter,  i.e.  one  cubic  decimeter  (see  Appendix). 
Place  upon  the  other  pan  some  body,  B,  which  will  just  counterbalance 

1  The  United  States  Government  carefully  preserves  in  Washington  copies  of  the 
international  meter.    These  are  declared  by  Congress  to  be  the  standard  units  of 
length  for  this  country. 

2  "  The  British  measurements  are  infinitely  inconvenient  and  wasteful  of  brain 
energy."  —  TAIT.     "  I  look  upon  our  English  system  as  a  wickedly  brain-destroying 
piece  of  bondage  under  which  we  suffer."  —  LORD  KELVIN. 


6  INTRODUCTION. 

the  empty  vessel.  Then  place  upon  the  same  pan  a  kilogram  mass,  C. 
Now  pour  water  slowly  into  the  vessel  until  the  water  and  kilogram  mass 
counterbalance  each  other.  What  mass  of  water  does  the  vessel  con- 
tain ?  How  does  the  mass  of  water  in  A  compare  with  the  mass  of  the 
body  C  ?  How  does  the  volume  of  water  compare  with  the  volume  of 
the  body  C  ? 

Mass  is  quite  distinct  from  weight.  The  weight  of  a  body 
is  the  measure  of  the  attraction  between  it  and  the  earth,  and 
may  vary  with  change  of  position,  because  the  earth's  attrac- 
tion varies  with  the  distance  of  the  body  from  the  earth,  while 
the  mass  of  the  body  remains  constant.  Mass  does  not  depend 
upon  weight,  but  weight  depends  upon  mass.  . 

When  we  open  a  heavy  iron  gate,  it  is  its  mass  with  which 
we  have  to  deal  ;  if  it  were  lying  on  the  ground  and  we 
should  try  to  raise  it,  we  should  have  to  deal  simultaneously 
with  both  its  mass  and  its  weight. 

The  process  of  measuring  the  mass  of  a  body  must  not  be 
confounded  with  the  process  of  finding  how  heavy  a 
body  is,  although  both  processes  are,  in  common  usage, 
called  weighing.      Weighing  a  body  to  ascertain  its 
mass  consists  in  balancing  it  with  a  body  or  bodies  of 
known   mass,  and  is  performed  with  a  scale  balance 
(Fig.  3)  and  a  set  of  masses  (commonly  called  a  set  of 
weights).      Weighing  to  ascertain  weight   should   be 
performed  with  an  instrument  adapted  to  measuring 
\J      force,  e.g.  a  spring  balance  (Fig.  4).     For  most  prac- 
FIG.  4.  tical  purposes,  however,  the  latter  instrument  may  be 
used  to  measure  mass,  inasmuch  as  at  the  same  place  mass  is 
proportional  to  weight.1 

Equal  volumes  of  different  substances  (e.g.  cork,  cheese,  lead) 
contain  unequal  quantities  of  matter.  Of  two  substances,  that 
which  contains  the  greater  quantity  of  matter  in  the  same 
volume  is  said  to  be  the  denser.  By  the  density  of  a  substance 

1  This  is  one  of  many  instances  in  physics  in  which  one  quantity  is  indirectly 
measured  by  measuring  another  proportional  to  it. 


THREE    STATES    OF    MATTER.  7 

is  meant  the  mass  in  a  unit  of  volume  of  that  substance.  The 
density  of  water  (at  4°  C.)  is  one  gram  per  cubic  centimeter, 
and  the  density  of  cast  iron  is  about  7.12  grams  per  cubic 
centimeter. 

The  mean  (or  average)  density  of  a  body  is  found  by 
dividing  its  mass  by  its  volume.  Thus,  if  the  mass  of  a  body 
be  32  g.  and  its  volume  be  5  cc.,  its  mean  density  is  (32  -s-  5  =) 
6.4  g.  per  cc. 

7.  Three  States  of  Matter.  Fluidity.  We  recognize  three 
states  or  conditions  of  matter,  viz.  solid,  liquid,  and  gaseous, 
distinctively  represented  by  earth,  water,  and  air.  Everyday 
observation  teaches  us  that  solids  tend  to  preserve  a  definite 
volume  and  shape;  liquids  tend  to  preserve  a  definite  volume 
only,  while  their  shape  conforms  to  that  of  the  containing  vessel  ; 
gases  tend  to  preserve  neither  definite  volume  nor  shape,  but  to 
expand  indefinitely. 

In  consequence  of  their  manifest  tendency  to  flow,  liquids 
and  gases  are  called  fluids. 

Susceptibility  of  motion  of  the  molecules  of  a  body  around 
and  among  one  another  is  called  fluidity.  All  bodies  of 
matter,  including  solids,  possess  this  property,  but  in  very 
different  degrees.  It  is  due  to  this  property  that  solids  can 
be  bent,  stretched,  and  compressed,  and  that  most  metals 
can  be  drawn  into  wires  and  rolled  or  hammered  into  sheets. 

EXERCISES. 

1.  (a)  Give  names  of  at  least  three  substances.     (6)  Give  a  name  of  a 
body  of  each  substance  named. 

2.  What   additional   idea  does  the  term    "impenetrability"  imply 
besides  extension  ? 

3.  How  may  it  be  shown  that  air  is  matter  ? 

4.  (a)  What  is  an  air  bubble  (e.g.  in  water)?     (6)  What  property  does 
it  show  that  air  possesses  ? 

5.  Why  is  matter  compressible  ? 


8  INTRODUCTION. 

6.  How  may  bodies  of  matter  be  expanded  ? 

7.  Heating  a  body  is  attended  with  what  molecular  changes  ? 

8.  (a)  Distinguish  between  the  mass  and  the  weight  of  a  body.     (6) 
Which  may  change,  and  why,  while  the  other  remains  constant  ? 

9.  Which  instrument  represented  in  Figs.  3  and  4  will  not  show  a 
change  of  weight  of  a  body  occasioned  by  a  change  of  distance  from  the 
earth  ? 

10.  (a)  Which  is  more  difficult,  to  roll  a  cannon  ball  along  a  smooth 
floor  or  to  raise  the  same  from  the  floor  ?     (6)  In  rolling  the  ball,  with 
which  do  we   deal,    its   mass  or  its  weight?     (c)   In  raising  the  ball, 
with  what  do  we  deal  ? 

11.  In  weighing  articles  of  groceries,  such  as  tea,  sugar,  etc.,  is  the 
purpose  to  measure  their  mass  or  the  force  of  gravity  ? 

12.  If  the  mass  of  45  cc.  of  cork  be  10.8  g.,  what  is  the  density  of 
cork? 

SECTION   II. 
KINEMATICS. 

8.  Kinematics,     Kinematics  treats  of  motions  without  ref- 
erence to  their  causes.     Nearly  all  physical  phenomena  are 
attributable  to  motions  (§  1),  hence  the  great  importance  of 
this  subject.     Motions  of  bodies  of  sensible  size  are  called 
molar  or  mechanical  motions   in   distinction   from   molecular 
motions.     The  motions  of  the  molecules  of  a  body  constitute 
its  heat,  and  will  therefore  be  treated  under  that  head. 

9,  Motion.     Motion  is  a  continuous  change  of  position.     That 
which  moves  is  known  as  matter.     The  position  of  a  particle 
of  matter  is  determined  by  its  direction  and  distance  from 
another  particle,  or  from  some  point  of  reference.     A  particle 
moves  relatively  to  a  given  point  while  an  imaginary  straight 
line  connecting  it  with  the  point  changes  either  in  direction  or 
in  length.     A  particle  is  at  rest  relative  to  a  given  point  while 
a  straight  line  joining  them  changes  neither  in  direction  nor 
in  length. 


MOTION. 


9 


When  you  open  or  shut  the  legs  of  a  pair  of  dividers  (A,  Fig.  5),  a 
straight  line,  a' b',  connecting  the  points  at  the  ends  of  the  legs  changes 
in  length;  hence  there  is  relative  motion  between- these  points.  If  (B, 
Fig.  5)  you  open  the  legs  a  little  way,  and,  fixing  the  end  of  one  of  the 
legs  upon  a  plane  surface,  trace  a  circle  with  the  end  of  the  other  leg 
around  the  former  as  a  center,  there  will  be  relative  motion  between  the 
two  points,  since  a  line  joining  them,  a  b,  a  b',  etc.,  changes  in  direction. 

If  (C,  Fig.  5)  you  trace  with  the  points  of  the  open  dividers  two 
straight  parallel  lines  on  a  plane  surface,  the  two  points  will  be  relatively 
at  rest,  just  as  surely  as  if  the  dividers  were  lying  upon  the  table,  since 
in  both  cases  a  straight  line  connecting  the  points  a  b,  a'b',  etc.,  changes 
neither  in  length  nor  in  direction. 


FIG.  5. 

A  point  may  be  at  the  same  instant  at  rest  with  reference  to  certain 
points  and  in  motion  with  reference  to  certain  other  points.  For 
example,  while  the  points  of  the  dividers  are  tracing  straight  lines  on 
the  plane  surface  (C,  Fig.  5),  and  are  relatively  at  rest,  they  are  in  motion 
with  reference  to  every  point  in  the  plane  surface.  A  passenger  in  a 
railway  car  may  be  at  rest  relative  to  the  car  and  the  other  passengers, 
but  in  rapid  motion  relative  to  objects  by  the  roadside. 

In  ordinary  language  the  phrase  "a  body  at  rest",  means  a  body 
that  does  not  change  its  position  with  reference  to  that  on  which  it 
stands,  as,  for  instance,  the  surface  of  the  earth  or  the  deck  of  a  ship. 
It  can  mean  nothing  else,  for  both  the  body  said  to  be  " at  rest"  and  all 


10  INTRODUCTION. 

points  on  the  earth's  surface  are  in  rapid  motion  with  reference  to  the 
sun  and  other  heavenly  bodies,  and  also  with  reference  to  the  earth's 
axis. 

10.  Velocity.  Velocity  is  rate  of  change  of  position.  It  in- 
volves units  of  distance  (or  length)  and  units  of  time,  and  is 
commonly  expressed  in  units  of  distance  per  unit  of  time,  e.g. 
feet  per  second,  miles  per  hour,  etc. 

If  a  particle  move  through  equal  distances  in  equal  periods 
of  time,  the  velocity  is  said  to  be  uniform.  If  the  distances 
traversed  in  equal  intervals  of  time  continually  increase  or 
continually  decrease,  the  velocity  is  said  to  be  accelerated. 

Velocity  is  determined  by  dividing  the  distance  traversed 
by  the  time  consumed.  If  a  body  move  s  feet  in  t  seconds,  its 

O  o 

velocity,  v,  is  -  feet  per  second,  or  v  =  - .    In  case  the  velocity 
t  t 

be  accelerated,  this  result  is  to  be  regarded  as  the  average 
velocity  for  that  distance;  and  in  the  case  of  uniform  motion 
the  average  velocity  is  the  same  as  the  actual  velocity  at  every 
instant.  It  is  evident  that  the  actual  velocity  of  a  body  whose 
rate  of  motion  changes  can  be  given  only  at  some  definite 
instant  or  point  in  its  journey.  It  denotes  the  space  which 
would  be  traversed  in  a  unit  of  time,  if  at  the  given  instant  the 
velocity  should  become  uniform. 

When  a  particle  experiences  equal  changes  of  velocity  in 
equal  units  of  time,  its  motion  is  said  to  be  uniformly  acceler- 
ated, and  its  change  of  velocity  per  unit  of  time  is  called  its 
rate  of  acceleration,  or  simply  its  acceleration,  and  is  repre- 
sented by  a.  When  the  velocity  increases,  as  in  the  case  of 
a  falling  stone,  its  acceleration  is  said  to  be  positive  (+  a) ; 
when  the  velocity  decreases,  as  in  the  case  of  a  stone  thrown 
upward,  its  acceleration  is  said  to  be  negative  (—  a). 

The  acceleration  of  a  body  falling  in  a  vacuum  and  of  a  body  pro- 
jected vertically  upward  in  a  vacuum  is  practically  uniform;  in  the  former 
case  it  is  about  32.2  feet  (or  9.8  m.)  per  second;  in  the  latter  case  it  is  a 
negative  acceleration  of  about  32.2  feet  per  second. 


ACCELERATED    MOTION.  11 

The  rate  of  acceleration  of  a  particle  in  traversing  a  certain 
distance  in  a  given  time  is  found  by  dividing  the  entire  change 
in  velocity,  v,  by  the  units  of  time,  t,  consumed  in  making  the 

v 

change  ;  i.e.  a  =  -,  whence  v  =  a  t. 
t 

Thus,  if  the  velocity  of  a  railroad  train  at  a  certain  instant  be  25  miles 
per  hour,  and  half  an  hour  hence  it  be  15  miles  per  hour,  then  the  entire 
change  of  velocity,  v,  is  —  10  miles  per  hour;  hence  the  average  accelera- 
tion, i.e.  the  acceleration  if  it  were  uniformly  distributed  throughout  the 

30  minutes,  is  —  —  -  =  (  —  -  J  of  a  mile  per  minute.     Again,  if  a  stone 

falling  with  a  uniformly  accelerated  velocity  acquire  in  4  seconds  a 

128  8 
velocity  of  128.8  feet  per  second,  its  acceleration  is  —  —  =  32.2  feet  per 

second. 

SECTION   III. 
LAWS   OF   UNIFORMLY   ACCELERATED   MOTION. 

11.  First  Law.  If  a  particle  starting  from  a  state  of  rest 
move  with  uniform  acceleration,  a,  its  velocity,  v,  at  the  end 
of  any  given  unit  of  time,  t,  is  found  by  the  equation  (1). 
v  —  a  t,  as  given  in  §  10.  From  this  equation  we  derive  the 
following  law:1 

Change  of  velocity  due  to  uniform  acceleration  is  equal  to  the 
product  of  the  acceleration  multiplied'  by  the  units  of  time  ;  or, 
the  change  of  velocity  is  proportional  to  the  rate  of  acceleration 
and  to  the  time  occupied. 

But  if  a  particle  be  in  motion,  and  at  a  certain  instant  have 
a  velocity,  V,  and  its  acceleration  be  a,  then  its  velocity  at 
any  subsequent  instant  is  expressed  as  follows: 


After  a  lapse  of  one  unit    of  time,         v  =  V^=.  (a  X  1). 
"     "     "       "  two  units  "      "  v  —  V^L  (a  X  2). 

"     "     "       "  t  "      "      "     (2)  v  =  V±at. 

1  A  physical  law  is  an  expression  of  the  relation  which  has  been  discovered  to 
exist  between  certain  physical  quantities. 


12 


INTRODUCTION. 


12.  Second  Law.  Since  the  velocity  of 
a  particle  starting  from  a  state  of  rest  in- 
creases from  zero  to  a  t,  the  average  velocity 

must  be  — - —  =  \  a  t.    At  this  rate  in  the 

same  time,  t,  it  would  traverse  a  distance,  S, 
equal  to  £  at  X  t  =  %  at2  units;  hence,  (3) 
8  =  ^atz.  From  this  we  derive  the  law: 

The  distance  traversed  in  a  given  time  by 
a  particle  starting  from  a  state  of  rest  and 
having  uniformly  accelerated  velocity  is  one 
half  the  product  of  the  acceleration  and  the 
square  of  the  units  of  time;  or,  the  entire 
distance  traversed  is  proportional  to  the  rate 
of  acceleration  and  to  the  square  of  the  time 
occupied. 

If  a  particle,  instead  of  starting  from  a 
state  of  rest,  have  an  initial  velocity,  V,  it 
would  move  in  t  units  of  time  without  accel- 
i  II  *      eration  a  distance  V  X  t ;   to  this  distance 
must  be  added  the    distance   it   moves  in 
consequence    of    acceleration,    in   order   to 
obtain   the   entire    distance  traversed  in  t 
•  H  units,  and  our  formula  becomes  (4) 


FIG.  6. 


If  it  be  required  to  find  the  distance 
passed  over  during  any  specified  unit  of 
time  we  may  subtract  the  distance  traversed 
in  t  —  1  units  from  the  distance  traversed 
in  t  units.  Thus,  representing  the  required 
distance  traversed  during  a  specified  unit 
of  time  t  by  s,  we  have  (5) 

s  =  ±  at2  -  %  a(t  -  I)2  -  %  a(2t  -  1). 


ACCELERATED    MOTION. 


13 


13,  Verification.  The  laws  given  above  are  verified  approximately 
and  conveniently  by  the  use  of  the  venerable  Atwood's  machine.1  The 
equal  weights  A  and  B  (Fig.  6)  are  suspended  by  a  thread  passing  over 
the  wheel  C.  Inasmuch  as  the  weights  are  equal,  they  counterbalance 
each  other  and  remain  at  rest.  Raise  the  weight  A  and  place  it  on  the 
platform  D  as  shown  in  Fig.  7.  Place  on  this 
weight  a  small  additional  one,  E,  called  a 
"rider,"  the  weight  of  which  sets  the  system 
in  motion.  Set  the  pendulum  F  swinging.  At 
each  swing  it  causes  a  stroke  of  the  hammer  on 
the  bell  G.  At  the  instant  of  the  first  stroke 
the  pendulum  causes  the  platform  D  to  drop  so 
as  to  allow  the  weights  to  move.  When  they 
reach  the  ring  H,  the  rider,  not  being  able  to 
pass  through,  is  caught  off  by  the  ring.  Raise 
and  lower  the  ring  on  the  graduated  pillar  I, 
and  ascertain  by  repeated  trials  the  average  dis- 
tance the  weights  move  between  the  first  two 
strokes  of  the  bell,  L  e.  during  one  swing  of  the 
pendulum.  Inasmuch  as  all  swings  of  the  pen- 
dulum are  made  in  equal  intervals  of  time,  we 
may  take  the  time  of  one  swing  as  a  unit  of 
time.  We  will  also,  for  convenience,  take  for  a 
unit  of  distance  the  distance  the  weights  move  during  the  first  unit  of 
time,  call  this  unit  a  space,  and  represent  the  unit  graphically  by  the 
line  a  b  (Fig.  8). 

Next  ascertain  how  far  the  weights  move  from  the  starting  point  during 
two  units  of  time,  i.e.  in  the  interval  of  time  between  the  first  and  third 
strokes  of  the  bell.  The  distance  will  be  found  to  be  four  spaces,  or 
four  times  the  distance  that  they  moved  during  the  first  unit  of  time. 
This  distance  is  represented  by  the  line  a  c. 

Now  ascertain  the  velocity  which  the  weights  have  at  the  end  of  the 
first  unit  of  time.  Place  the  ring  H  at  the  point  (b,  Fig.  8)  which  the 
weights  have  been  found  by  trial  to  reach  at  the  end  of  the  first  unit  of 
time.  Allow  the  weights  to  descend  as  before.  At  the  end  of  the  first 
unit  of  time  the  rider  is  caught  off.  At  this  instant  acceleration  ceases, 
and  the  motion  becomes  uniform.  Ascertain  how  far  the  weights  move 
with  uniform  velocity  during  the  second  unit  of  time ;  this  velocity  is 
evidently  the  velocity  which  the  weights  have  at  the  end  of  the  first  unit 

1  This  machine  is  a  contrivance  which  enables  us  to  increase  the  mass  to  be  moved 
without  increasing  the  force  which  moves  it,  thus  so  decreasing  the  acceleration  as  to 
render  approximate  measurements  feasible. 


FIG.  7. 


14 


INTRODUCTION. 


1  U.ofT. b- 


S  U.ofT. c 


3  U.ofT.  _____d- 


...  1  space. 

. . .  Represents  the  velocity  at  the  end  of  the  first  unit 
of  time ;  also  the  acceleration  during  the  first 
unit  of  time. 


. . .  Velocity  at  the  end  of  the  second  unit  of  time. 
. . .  Acceleration  during  the  second  unit  of  time. 


„ . . .  Velocity  at  the  end  of  the  third  unit  of  time. 


. . .  Acceleration  during  the  third  unit  of  time. 


4  U.ofT. e^ 

FIG.  8. 

of  time.  This  distance  will  be  found  to  be  (approximately  l)  two  spaces  ; 
hence  the  velocity  at  the  end  of  the  first  unit  of  time  is  two  spaces  per 
unit  of  time.  But  the  velocity  at  the  beginning  of  the  first  unit  of  time 
was  zero  ;  hence  the  acceleration  during  the  first  unit  of  time  is  two  spaces 
per  unit  of  time. 

In  like  manner  determine  the  velocity  at  the  end  of  the  second  unit  of 
time.  It  will  be  found  to  be  four  spaces  per  unit  of  time.  And  as  the 
velocity  at  the  end  of  the  first  unit  of  time  was  two  spaces  per  unit  of 
time,  the  acceleration  during  the  second  unit  of  time  is  two  spaces  per 
unit  of  time.  Hence  the  acceleration  during  the  first  two  units  of  time  is 
uniform,  and  the  change  of  velocity  during  the  first  two  units  of  time,  as 
stated  in  the  First  Law,  =  at  =  2  X  2  =  4  spaces  per  unit  of  time. 


1  Approximately,  since  they  are  retarded  by  the  resistance  of  the  air  and  the  fric- 
tion of  the  wheel. 


EXEKCISES.  15 


EXERCISES. 

1.  (a)  What  is  the  meaning  of  the  statement  that  "the  velocity  of  a 
falling  body  at  the  end  of.  the  first  second  of  its  fall  is  32.2  feet  per 
second  "  ?     (6)  Has  the  body  the  same  velocity  at  any  other  point  ? 

2.  What  is  the  relation  between  the  velocity  of  a  freely  falling  body  at 
the  end  of  the  first  unit  (of  time)  of  its  fall  and  its  acceleration  ? 

3.  The  velocity  of  a  particle  at  a  certain  instant  is  V ;  its  acceleration 
is  a.     What  will  be  its  velocity,  u,  in  t  units  of  time  afterward  ? 

4.  If  the  initial  velocity  of  a  body  be  F,  its  acceleration  a,  and  its  final 
velocity  •»,  how  long,  t,  was  it  in  acquiring  its  final  velocity  ? 

5.  If  a  body  having  an  initial  velocity  F  acquire  in  t  seconds  a  velocity 
u,  what  is  its  acceleration  ? 

6.  If  a  body  move  from  a  state  of  rest  with  a  uniform  acceleration  a, 
what  space,  *S,  will  it  traverse  in  t  units  of  time  ? 

7.  If  a  body  move  from  a  state  of  rest  with  an  acceleration  a,  in  what 
time,  £,  will  it  traverse  the  space  S  ? 

8.  The  .velocity  of  a  particle  at  a  certain  instant  is  20  feet  per  second; 
its  acceleration  is  3  feet  per  second.    What  will  be  its  velocity  10  seconds 
hence?  y       fa   /^  ^ 

9.  Suppose  that  the  acceleration  of  the  particle  mentioned  above  be 
—  2  feet  per  second,  what  will  be  its  velocity  5  seconds  after  the  instant 
named  ? 

10.  (a)  A  body  falls  from  a  state  of  rest ;  its  velocity  increases  (if  we 
disregard  the  resistance  of  the  air)  32.2  feet  per  second.     What  is  its 
velocity  at  the  end  of  the  first  second  ?     (6)  What  at  the  end  of  the 
tenth  second  ?    {c)  What  at  the  end  of  half  a  second  ? 

11.  If  the  initial  velocity  of  a  body  be  5  feet  per  second,  its  final 
velocity  25  feet  per  second,  and  its  acceleration  2  feet  per  second,  what 
was  the  time  consumed  in  acquiring  the  final  velocity  ? 

12.  A  bullet  is  projected  vertically  upward  with  an  initial  velocity  of 
161  feet  per  second.     What  will  be  its  velocity  at  the  end  of  the  third 
second  (a  =  —  33.2  feet  per  second)? 

13.  How  long  will  the  bullet  named  in  the  last  problem  rise  ? 

14.  What  velocity  will  the  bullet  have  at  the  end  of  the  sixth  second, 
and  in  what  direction  will  it  be  moving  ? 

15.  A  person  throws  a  stone  vertically  upward  to  a  distance  of  78.4 
meters.     With  what  velocity  does  the  stone  leave  his  hand  ? 


16  INTRODUCTION. 

16.  A  stone  thrown  vertically  downward  is  given  an  initial  velocity  of 
40  feet  per  second.     How  far  will  it  descend  in  10  seconds  ? 

17.  (a)  A  bullet  is  projected  vertically  upward  with  an  initial  velocity 
of  225.4  feet  per  second.    How  long  will  it  rise  ?    (6)  How  far  will  it  rise? 

18.  How  long  will  it  take  a  body  to  fall  from  a  state  of  rest  1030.4 
feet? 

19.  (a)  A  body  falls  during  1£  seconds.     What  is  its  final  velocity  ? 
(b)  How  far  does  it  fall  ? 

20.  A  body  falls  297.6  feet  in  4  seconds.     What  was  its  initial  velocity  ? 

Ans,  10  feet  per  second. 

21.  What  initial  velocity  must  be  given  a  body  that  it  may  rise  6 
seconds  ? 

22.  A  falling  body  acquires  a  velocity  of  68.6  meters  per.  second.  How 
long  does  it  fall  (a  =  9.8  meters)? 

23.  A  body  acquires  in  falling  a  velocity  of  98  meters  per  second. 
From  what  hight  has  it  fallen  ? 

24.  A  body  is  projected  vertically  upward  with  a  velocity  of  128.8  feet 
per  second.     Where  will  it  be  at  the  end  of  8  seconds  ? 

25.  (a)  A  body  at  rest  receives  a  uniform  acceleration  of  10  meters  per 
minute.     How  far  will  it  move  in  half  an  hour  ?     (b)  What  will  be  its 
velocity  at  the  end  of  the  half-hour  ? 

26.  A  R.,one  is  thrown  vertically  upward  with  a  velocity  of  100  meters 
per  second.     In  how  many  seconds  will  it  return  to  its  original  position  ? 

27.  (a)  In  what  time  would  a  stone  fall  to  the  earth  from  a  balloon 
3  miles  high  ?     (b)  What  velocity  would  it  acquire  ? 

28.  A  body  starts  from  a  state  of  rest  and  moves  with  a  uniform 
acceleration  of  18  feet  per  second.     Find  the  time  required  to  traverse 
the  first  foot. 

29.  A  stone  dropped  from  a  hight  of  4  feet  will  reach  the  ground  in 
what  time  ? 

30.  Find  the  depth  of  a  well  in  which  a  stone,  if  dropped,  takes  1| 
seconds  to  reach  the  bottom. 

31.  A  body  falls  from  a  state  of  rest,     (a)    How  many  feet  does  it  fall 
during  the  fifth  second  ?     (b)    How  many  meters  does  it  fall  during  the 
fourth  second  ? 

32.  How  far  does  the  stone  referred  to  in  Exercise  16  descend  during 
the  tenth  second  ? 


MOTIONS    AND    VELOCITIES.  17 


SECTION   IV. 

COMPOSITION    AND    RESOLUTION    OF    MOTIONS    AND 
VELOCITIES. 

14,  Graphical  Representation  of  Motion  and  of  Velocity.     A 

person  who  would  describe  to  you  the  motion  of  a  ball  struck 
by  a  bat  must  tell  you  three  things  : l  (1)  where  it  starts,  (2) 
in  what  direction  it  m-oves,  and  (3)  how  far  it  goes.  These 
three  essential  elements  may  be  represented  graphically  by  a 
straight  line.  Thus,  suppose  balls 
at  A  and  D  (Fig.  9)  to  be  struck  by 

bats,  and    to   move  respectively  to    D > E 

B  and  E  in  one  second.     Then  the 

points  A  and  D  are  their  starting  points,  the  lines  A  B  and 
D  E  represent  the  direction  of  their  motions,  and  the  lengths 
of  the  lines  represent  the  distances  traversed.  The  lengths 
of  these  lines  are  not  equal  to  the  distances  traversed  by  the 
two  balls,  but  represent  these  distances  drawn  to  some  con- 
venient arbitrary  scale ;  thus  on  a  scale  of  1  cm.  =0=  10  m., 
these  lines  represent  distances  of  32  m.  and  20  in.,  respec- 
tively. 

The  velocity  of  a  moving  body  is  described  by  giving  (1)  the 
direction  of  its  motion,  and  (2)  the  units  of  distance  traversed 
per  unit  of  time.  Since  the  lines  A  B  and  D  E  represent  the 
distances  traversed  by  the  two  balls  during  the  same  unit  of 
time,  these  lines  likewise  represent  their  average  velocities  dur- 
ing this  time;  i.e.  A  B  may  represent  an  average  velocity  of  32 
m.  per  second,  and  D  E  an  average  velocity  of  20  m.  per  second. 

15.  Composition  of  Simultaneous  Motions  and  Velocities. 

If  by  any  means  a  particle  have  two  or  more  separate  and 
independent  motions  communicated  to  it  simultaneously,  and 
if  the  motions  imparted  be  themselves  constant  in  velocity 

1  It  is  assumed  that  the  motion  is  rectilinear. 


INTRODUCTION. 


and  direction,  the  result  of  the  two  motions  is  a  single  motion 
in  a  straight  line  with  a  single  velocity  and  direction. 
This  is  illustrated  in  the  following  manner  : 

With  the  handle  A  in  the  position  shown  in  Fig.  10,  push  it  forward, 
carrying  the  frame  B  C  to  the  right.  This  frame  carries  a  pencil,  D, 
whose  point  presses  the  paper  below,  and  as  the  frame  advances  the 
line  a  b  is  traced  upon  the  paper,  graphically  representing  the  motion 
of  the  pencil.  If,  when  the  pencil  point  is  at  a  and  the  frame  is  at  rest, 
the  string  G  be  pulled,  the  pencil  will  trace  the  line  a  c  at  right  angles 
to  a  b.  Now  these  two  independent  motions  may  be  communicated  to 


FIG.  10. 

the  pencil  simultaneously  by  fastening  the  string  E  to  the  binding  screw 
F  and  pushing  forward  the  handle  A.  The  pencil  point  will  not  move  in 
either  of  tl.e  lines  a  b  or  a  c,  but  its  motion  will  be  intermediate  between 
the  two,  and  it  will  trace  the  line  a  d.  This  single  motion,  which  is  the 
result  of  the  concurrence  of  two  motions,  is  called  their  resultant ;  and 
they,  with  regard  to  the  resultant,  are  called  its  components. 

The  distance  a  d  is  traversed  in  exactly  the  same  time  that  the  distance 
a  b  would  be  traversed  if  the  pencil  had  no  other  motion,  the  handle  A 
being  pushed  forward  with  the  same  speed  in  both  cases ;  likewise  the 
distance  a  d  is  traversed  in  the  same  time  that  the  distance  a  c  is  accom- 
plished when  the  string  is  simply  pulled 
over  the  pulley  G  with  the  same  speed, 
and  has  no  other  motion.  The  lines 
a  b,  a  c,  and  a  d  represent  not  only  the 
distances  traversed  in  the  several  direc- 
tions, but  also  the  magnitudes  and  direc- 
tions of  the  respective  velocities.  For 
example,  if  the  velocity  be  constant  and 
the  pencil  reach  successively  at  the  end 


FIG.  11. 


of  equal  intervals  of  time  the  points  m",   n",    and  d   (Fig.   11),  then 
a  m",  m"  n",  and  n"  d  represent  its  velocities  in  the  successive  intervals, 


RESOLUTION    OF   MOTION. 


19 


arid  am,  m  n,  and  n  b  represent  the  velocities  for  the  same  intervals  in 
the  direction  a  b;  and  a  m',  m'  n',  and  n'c  the  velocities  in  the  direction 
a  c.  If  points  c  and  d,  and  d  and  b  be  joined  by  (dotted)  lines,  we  have 
a  parallelogram  of  which  the  line  ad,  representing  the  resultant,  is  a 
diagonal. 

Hence,  to  find  the  resultant  of  two  simultaneous  velocities 
when  they  make  an  angle  with  each  other,  the  rule  is :  Con- 
struct a  parallelogram  of  which  the  adjacent  sides  represent  the 
two  velocities;  then  the  diagonal  which  lies  between  these  adjacent 
sides  represents  their  resultant. 

When  more  than  two  components  are  given,  find  the  resultant 
of  any  two  of  them,  then  of  this  resultant 
and  a  third,  and  so  on  until  every  com- 
ponent has  been  used.  For  example,  let 
the  several  velocities  imparted  to  a 
particle  be  represented  by  the  lines  A  B, 
AC,  A  D,  and  A  E  (Fig.  12).  The  result-  B« 
ant  of  A  B  and  AC  is  A  F;  the  resultant 
of  A  F  and  AD  is  A  G ;  that  of  A  G  and 
A  E  is  A  H,  which  represents  the  result- 
ant of  the  four  velocities, 

When  two  components  are  at  right  angles  to  each  other,  it  is  evident 
that  we  may  obtain  the  magnitude  of  the  resultant  by  finding  the  square 
root  of  the  sum  of  the  squares  of  the  two  components. 

In  case  a  particle  has  several  velocities  imparted  to  it,  all  in  the  same 
direction,  their  resultant  is  the  sum  of  all.  If  some  are  opposite  to  others, 
one  of  the  two  directions  is  considered  as  positive  and  the  opposite  direc- 
tion as  negative,  and  these  signs  being  prefixed  to  the  numerical  values, 
their  algebraic  sum  is  the  resultant. 

16.  Resolution  of  a  Motion  or  a  Velocity  into  Components. 

Any  motion  or  velocity  may  be  resolved  into  D 
two  or  any  given  number  of  motions  or  veloc- 
ities. Let  A  B  (Fig.  13)  represent  the  velocity 
and  direction  of  motion  of  a  particle.  Draw 
a  line,  A  C,  to  represent,  either  arbitrarily  or 
according  to  the  conditions  of  the  problem,  VlQt  13. 


20 


INTRODUCTION. 


one  of  the  required  components.  Connect  B  and  C,  draw  A  D 
parallel  to  B  C,  and  D  B  to  A  C,  and  thus  complete  a  parallelo- 
gram of  which  A  B  is  a  diagonal.  The  two  adjacent  sides 
A  C  and  A  D  represent  two  component  velocities  of  the  particle  ; 
in  other  words,  a  particle  having  a  velocity  represented  by 
the  line  A  B  has  at  the  same  time  velocities  represented  in 
magnitude  and  direction  by  the  lines  A  C  and  A  D. 

17.  Composition  of  Constant  with  Accelerated  Velocity, 
Experience  teaches  that  a  body,  e.g.  a  stone,  projected  in  a 
horizontal  direction  moves,  not  in  a  horizontal  path,  but  in  a 
path  intermediate  between  a  horizontal  and  a  vertical  one, 
showing  that  its  velocity  is  composed  of  a  horizontal  and  a 


FIG.  14. 

vertical  component.  Its  horizontal  velocity  (if  the  resistance 
of  the  air  be  disregarded)  is  constant  and  its  vertical  velocity 
is  uniformly  accelerated.  Let  A  B  (Fig.  14)  represent  the  ver- 
tical component  of  the  motion  during  the  first  second ;  then 
B  C  and  C  D  will  represent  its  vertical  motion  during  the  sec- 
ond and  third  seconds,  respectively.  Let  A  B',  B'C',  and  C'D' 
represent  successive  horizontal  motions  during  the  same  three 


EXERCISES.  21 

periods.  Then  by  the  law  of  the  composition  of  motions  it  is 
evident  that  the  body  will  pass  from  A  to  B"  during  the  first 
second,  from  B"  to  C"  during  the  second  second,  and  from  C" 
to  D"  during  the  third  second.  The  body  traverses  a  curvi- 
linear path  called  a  parabola,  as  shown  in  the  figure.  In 
practice,  the  resistance  of  the  air  would  modify  the  nature 
of  the  curve  somewhat,  so  that  its  real  path  is  a  peculiar 
curve  known  in  the  science  of  gunnery  as  a  ballistic  curve  or 
trajectory.1 

It  should  be  borne  in  mind!  that  one  of  the  component  veloci- 
ties of  a  particle  moving  in  a  curvilinear  path  is  always  acceler- 
ated. 

EXERCISES. 

1.  (a)  If  a  ship  move  east  at  the  rate  of  10  miles  an  hour,  and  a  per- 
son on  deck  walk  towards  the  bow  at  the  rate  of  2  miles  an  hour,  what  is 
the  resultant  of  these  two  velocities  ?     (6)  With  reference  to  what  has  he 
this  velocity  ? 

2.  (a)  Suppose  the  person  on  the  ship  mentioned  above  to  walk  aft  at 
the  rate  of  2  miles  an  hour,  what  will  be  the  resultant  of  the  two  veloc- 
ities ?     (6)  Prefix  suitable  signs  to  the  numbers  given  and  represent  the 
addition  which  gives  the  resultant. 

3.  Suppose  the  person  to  walk  directly  north  across  the  deck  at  the 
rate  of  4  miles  an  hour,  what  will  be  the  resultant  of  the  two  velocities  ? 

4.  Suppose  the  person  to  walk  northeast  at  the  rate  of  4  miles  an  hour, 
what  will  be  his  resultant  velocity  ?     [In  drawing  the  parallelogram  of 
velocities,  represent  the  component  velocities  to  some  scale,  e.g.  i  of  1 
inch  or  1  cm.  =c=l  mile;  then,  having  completed  the  parallelogram  and 
having  drawn  the  diagonal  which  represents  the  resultant,  measure  the 
latter,  and  the  result  will  express,  on  the  scale  chosen,  the  resultant 
velocity  required.] 

5.  Suppose  an  attempt  to  be  made  to  row  a  boat  at  the  rate  of  6  miles 
an  hour  directly  across  a  stream  flowing  at  the  rate  of  10  miles  an  hour, 
determine  the  direction  and  velocity  of  the  boat. 

•  1  If  the  velocity  of  a  projectile  be  very  great,  the  trajectory  at  first  will  be  very 
fiat.  For  example,  if  the  initial  velocity  of  a  rifie  bullet  be.  2550  feet  a  second,  the 
vertical  component  of  the  trajectory  for  tb«%  first  1500  feet  may  not  be  more  than  2£ 
feet. 


22  INTRODUCTION. 

6.  A  vessel  sails  south-southeast  (i.e.  22.5°  east  of  south)  at  the  rate 
of  14  miles  an  hour.     Determine  its  southerly  and  its  easterly  velocity. 

7.  Represent  graphically,  to  scale,  a  velocity  of  100  feet  per  second, 
and  resolve  this  velocity  into  two  components  which  shall  have  between 
them  an  angle  of  45°. 

8.  Imagine  a  body  to  be  projected  obliquely  upward  at  an  angle  of 
i  45°.     Represent  arbitrarily  its  vertically  downward  accelerated  motion, 
'  and  its  obliquely  upward  constant  motion  for  3  seconds,  and  determine 

the  actual  path  traversed  by  the  body  during  this  time. 
~      9.    When  a  ship  is  sailing  northeast  at  the  rate  of  10  miles  per  hour, 
with  what  speed  is  it  approaching  a  north  and  south  coast  lying  to  the 
east  ?  Ans.  7.071  miles  per  hour. 


SECTION  V. 

KINDS   OF   MOTION. 

18.  Motion  of  Translation  and  of  Rotation.  In  pure  motion 
of  translation  all  the  points  of  a  body  move  with,  the  same 
velocity  and  in  the  same  direction  (Fig.  15).  Example :  the 


A 


FIG.  15.  FIG.  16. 

Rectilinear  motion  of  translation.  Motion  of  rotation. 

motion  of  an  elevator,  or  of  a  piston  in  the  cylinder  of  a  sta- 
tionary steam  engine.  When  the  points  of  a  body  describe  arcs 
of  circles,  the  motion  is  one  of  rotation  (Fig.  16).  Example  : 
the  motion  of  a  top,  or  of  a  wheel  in  a  watch.  When  a  body 
rotates,  every  particle  in  the  body  describes  a  circle  round 
some  point  in  a  straight  line  which  forms  the  axis  of  rotation. 
The  velocity  of  a  point  far  from  the  axis  is  greater  than 
that  of  a  point  nearer  the  axis,  and,  generally,  the  velocity  of 
a  point  is  proportional  to  its  distance  from  the  axis ;  hence 
the  expression  " velocity  of  a  rotating  body"  is  meaningless. 


RECTILINEAR    AND    CURVILINEAR    MOTION. 


23 


We  may,  however,  speak  of  the  angular  velocity  of  the  rotating 
body,  which  is  the  same  for  all  points  in  the  body.  Angular 
velocity  is  rate  of  rotation,  and  is  measured  by  the  angle 
through  which  the  rotating  body  turns  in  any  given  unit  of 
time. 

19.  Rectilinear  and  Curvilinear  Motion.      Besides  change 
in  velocity,  there  may   be  a  change  in  direction  of  motion. 
When  a  particle  moves  in  a  constant  direction,  i.e.  in  a  straight 
line,  as  in  the  case  of  a  freely  falling  bullet,  its  motion  is  said 
to  be  rectilinear.     But   if   its  motion  constantly  changes   in 
direction,  i.e.  at  every  point,  as 

is  the  case  of  every  particle  in 
a  rotating  wheel  (except  points 
on  its  axis),  its  motion  is  said 
to  be  curvilinear.  It  is  evident 
that  the  direction  of  a  motion 
in  a  curvilinear  path  can  be 
given  only  for  some  specified 
point ;  and,  furthermore,  that  FlG-  17- 

the  direction  can  be  represented  only  by  a  straight  line, 
for  a  curved  line  is  a  line  having  an  infinite  number  of  direc- 
tions. 

Let  A  (Fig.  17)  represent  a  body  mounted  on  a  cardboard  sector,  S  S', 
which  is  rotated  about  the  axis  C  in  the  direction  indicated  by  the  arrow. 
The  body  will  move  in  the  circular  path  A  D  E  F.  The  straight  line  A  B 
will  indicate  the  direction  of  the  motion  at  every  point,  but  it  will  be 
seen  that  this  line  changes  its  direction  constantly.  At  whatever  point 
the  body  may  be  at  any  instant,  the  line  A  B,  which  shows  the  direction 
of  the  motion,  is  tangent  to  the  curve  at  that  point. 

20.  Analysis  of  Circular  Motion.     If  a  particle  move  in  a 
circular  path,  e.g.  a  stone  whirled  in  a  sling,  its  motion  every 
instant  is  the  resultant  of  a  tangential  motion  and  a  centrip- 
etal (toward  the  center)  motion.     If  when  it  passes  point  A 
(Fig.  18)  its  tangential  velocity  be   represented  by  A  B,  its 


24 


INTRODUCTION. 


FIG.  18. 


centripetal  velocity  may  be  represented  by 
B  C,  because  at  the  end  of  the  unit  of  time 
in  which  it  would  reach  B  if  it  were  mov- 
ing in  a  straight  line,  it  is  found  to  be  not 
at  B,  but  at  some  other  point,  C,  nearer 
the  center  by  the  distance  B  C.  The  cen- 
tripetal motion  is  an  accelerated  motion 

(§  17> 


EXERCISES. 

1.  What  kind  of  motion  is  that  of  the  earth  in  its  orbit  ? 

2.  Why  is  it  meaningless  to  speak  of  the  velocity  of  rotation  of  a 
body? 

3.  (a)  What  motions  have  the  wheels  of  a  carriage  that  is  drawn 
straight  along  a  level  plane  ?     (6)  What  motion  has  the  carriage  ? 

4.  Compare   the  several  velocities  of  the  small  front  wheels  of  the 
carriage  with  those  of  the  larger  hind-  wheels. 

5.  (a)  Can  there  be  motion  without  direction  ?     (&)  How  is  the  direc- 
tion of  the  motion  of  a  particle,  when  moving  in  a  curve,  represented  ? 

6.  How  is  the  angular  velocity  of  the  earth's  motion  about  its  axis 
expressed  ? 

7.  (a)  What  two  kind's  of  motions  has  the  earth?     (6)   Are  they 
rectilinear  or  curvilinear  ? 

8.  A  railway  car  moves  from  west  to  east  at  the  rate  of  10  miles  per 
hour,  and  a  man  walks  through  the  car  from  the  rear  toward  the  front  of 
the  car  at  the  rate  of  4  miles  per  hour.     At  what  rate  is  he  moving  east  ? 

9.  A  ship  is  sailing  due  south  at  the  rate  of  14  miles  an  hour,  and  a 
man  is  running  due  north  on  its  deck  at  the  rate  of  6  miles  an  hour.     In 
what  direction  is  the  man  moving  (i.e.  toward  the  north  or  the  south), 
and  at  what  rate  ? 

10.  A  body  moves  in  a  certain  direction.     Has  it  a  component  at  right 
angles  to  that  direction  ? 

11.  If  a  body  move  in  a  circular  path  (e.g.  a  stone  whirled  in  a  sling) 
its  motion  every  instant  is  compounded  of  motions  in  what  two  direc- 
tions ? 

12.  A  body  moves  due  northeast  at  the  rate  of  20  miles  per  hour. 
What  is  its  northerly  and  what  its  easterly  velocity  ? 


CHAPTER   II. 
MOLAR  DYNAMICS. 


SECTION   I. 
FOftCE. 

21.  Dynamics.     Dynamics  is   the   science  which  treats  of 
the    "  circumstances   under    which    particular    motions   take 
place.7'     This    science    will    be   treated   under   three   heads: 
(1)  Molar  Dynamics,  —  that  is,  the  dynamics   of  solids  and 
fluids,  including  the  study  of  sound  waves ;   (2)  Molecular 
Dynamics,  including    heat;    (3)  Ether   Dynamics,  —  that  is, 
radiation,  including  light  and  electricity. 

The  term  Physics  is  a  generic  term  which  includes  all 
these  branches  ;  i.e.  Physics  is  the  science,  which  treats  of  the 
dynamics  of  masses,  molecules,  and  the  ether. 

22.  Force  Defined.     When  a  body  at  rest  is  set  in  motion, 
or  one  which  is  in  motion  has  that  motion  accelerated  (posi- 
tively or  negatively),   or  when  a  moving  body  is  deflected 
from  a  straight  course,  experience  teaches  us  that  there  is 
always  a  cause,  and  we  have  also  learned  to  apply  to  this 
cause  the  name  force. 

FORCE  IS  THAT  WHICH  CHANGES,  OR  TENDS  TO  CHANGE,  A 
BODY  FROM  ITS  STATE  OF  REST  OR  OF  UNIFORM  MOTION  IN 
A  STRAIGHT  LINE. 

The  inference  from  this  definition  is  that  no  force  is  required 
to  keep  a  free  body *  moving  with  uniform  velocity  in  a  straight 
line,  but  that  force  is  required  to  change  its  motion  either  in 
magnitude  or  in  direction. 

1  By  a  free  body  is  meant  a  body  that  for  convenience  is  supposed  to  be  free  from 
the  action  of  all  resisting  forces  such  as  friction,  resistance  of  the  air,  etc. 


26  MOLAJB   DYNAMICS. 

It  cannot  be  directly  shown  that  a  moving  body,  if  left  to  itself,  would 
continue  to  move  forever  with  uniform  velocity  in  a  straight  line;  for  com- 
mon experience  affords  us  no  examples  of  bodies  moving  in  this  manner. 
The  reason  is  that  it  is  practically  impossible  to  isolate  a  body  from  the 
action  of  force.  But  we  have  abundant  evidence  that  the  more  nearly  a 
body  is  freed  from  the  action  of  force,  the  more  nearly  will  it  continue  to 
move  uniformly  in  a  straight  line.  Example  :  a  stone  projected  along  a 
sheet  of  smooth  ice. 

23.  Strain  and  Stress,     When  force  is  applied  to  a  body, 
in  addition  to  producing  motion  of  the  body  as  a  whole  it 
has  another  effect :  it  changes,  to  a  greater  or  less  degree,  the 
shape   and   possibly  the  size  of   a  body,  producing  relative 
motion  of  its  parts,  even  when  no  motion  of  the  body  as  a 
whole  ensues.     Examples :  the  deformation  caused  by  force 
in  a  bow  when  bent,  in  a  cord  when  twisted,  in  a  rubber  band 
when  stretched,  in  soft  bodies  like  jelly  when  pressed,  and  in 
air  when  compressed. 

When  the  form  or  volume  of  a  solid  body  is  temporarily 
changed,  owing  to  the  action  of  force,  the  body  is  said  to  be 
in  a  state  of  strain.  Owing  to  the  strain,  forces  tending  to 
resist  further  strain  are  called  into  play  within  the  body.  The 
name  stress  is  given  to  such  forces.  When,  holding  the  ends 
of  a  rubber  band  in  your  two  hands,  you  pull  it,  you  observe 
an  elongation  or  strain,  and  you  feel  not  only  a  resistance  to 
further  stretching,  but  also  a  force  drawing  your  hands  toward 
each  other.  This  is  stress  in  the  band. 

24.  Rigidity.     The  amount  of  deformation  which  a  given 
force  will  produce  depends  largely  upon  the  nature  of  the 
material.     A  great  force  is  required  to  change  the  shape  of  a 
body  of  iron,  while  the  force  required  to  produce  the  same 
change  in  a  body  of  jelly  is  very  small. 

Rigidity  is  the  name  given  to  the  property  of  solid  bodies 
which  enables  them  to  offer  resistance  to  change  of  shape. 
A  fluid  is  a  body  of  matter  which  possesses  no  rigidity. 


NEWTON'S  FIRST  LAW  OF  MOTION.  27 

SECTION   II. 

NEWTON'S  THKEE  LAWS  OF  MOTION  OB  AXIOMS. 
MOMENTUM. 

The  relations  between  matter  and  force  are  concisely  ex- 
pressed in  what  are  known  as  The  Three  Laws  of  Motion,  first 
enunciated  by  Sir  Isaac  Newton. 

25.  Newton's  First  Law  of  Motion,    Inertia.      A  body    at 
rest  remains  at  rest,  and  a  body  in  motion  moves  with  uniform 
velocity  in  a  straight  line,  unless  acted  upon  by  some  external 
force. 

A  body  is  said  to  be  acted  upon  by  an  "  external  force " 
when  the  action  is  between  that  body  and  some  other  body  (in 
contradistinction  to  an  action  between  parts  of  the  same 
body).  This  law  expressly  declares  that  any  change  in  the 
motion  of  a  body,  whether  of  velocity  or  of  direction,  indi- 
cates the  presence  of  an  external  force. 

The  inability  of  matter  to  change  the  state  that  it  is  in, 
whether  it  be  of  motion  or  of  rest,  or,  in  other  words,  the 
property  in  virtue  of  which  external  force  is  required  to  change 
the  velocity  of  a  body,  is  called  inertia;1  hence,  the  First  Law 
of  Motion  is  often  called  the  "  Law  of  Inertia.'7 

The  backward  motion  of  passengers  when  a  car  is  suddenly  started, 
and  their  forward  motion  when  the  car  is  suddenly  stopped,  the  difficulty 
in  starting  a  vehicle  and  the  comparative  ease  of  keeping  it  in  motion 
after  it  is  put  in  motion,  and  the  ceaseless  motion  of  the  planets  are  due 
to  inertia. 

26.  Momentum.     We  know  that  some  moving  bodies  are 
stopped  much  more  easily  than  others.       An  empty  car  is 
stopped  much  more  easily  than  a  loaded  car.     It  is  compara- 
tively easy  to  set  a  small  cricket  ball  rolling  along  the  ground 

1  "  Matter  is,  as  it  were,  the  plaything  of  force  ;  submitting  to  any  change  of 
state  that  may  be  impressed  upon  it,  but  rigorously  persevering  in  the  state  in  which 
it  is  left  until  force  again  acts  upon  it."  —  TAIT. 


28  MOLAK   DYNAMICS. 

with  considerable  velocity,  but  to  set  a  large  cannon  ball 
rolling  with  the  same  speed  requires  much  effort.  And  while 
we  can  easily  stop  the  former  when  it  is  thrown  to  us,  we 
should  find  it  very  difficult  to  stop  the  latter  traveling  at  any- 
thing like  the  same  speed. 

This  difference  cannot  be  due  to  difference  of  weight  of  the 
balls,  for,  as  we  do  not  lift  them  off  the  ground,  we  are  not 
obliged  to  overcome  their  weight.  The  forces  required  to  pro- 
duce the  same  change  of  velocity  in  different  bodies  are  propor- 
tional to  their  masses,  provided  the  forces  act  for  the  same  time. 

Mass  may  be  said  to  measure  inertia,  or  passivity,  i.e.  the  property  in 
virtue  of  which  more  or  less  force  is  required  to  change  the  velocity  of  a 
body.  Conversely,  inertia  is  the  measure  of  mass.  In  fact,  the  terms 
mass  and  inertia  are  often  used  interchangeably. 

Again,  we  have  an  instinctive  dread  of  bodies  of  small  mass 
when  moving  with  great  speed.  A  ball  tossed  is  a  different 
affair  from  a  ball  thrown. 

Thus  we  are  led  to  the  consideration  of  a  complex  quantity 
called  momentum.  The  momentum  of  a  body  is  a  quantity 
measured  by  the  product  of  its  mass  and  its  velocity.  A  unit  of 
momentum  is  the  momentum  of  a  unit  mass  moving  with  a 
unit  velocity. 

If  the  measures  of  the  mass  and  the  velocity  of  a  body  be  m  and  i>, 
respectively,  the  product  m  u,  or  momentum  of  the  body,  has  m  v  times 
the  momentum  of  a  unit  mass  moving  with  unit  velocity.  Thus,  if  the 
momentum  of  a  mass  of  1  k.  having  a  velocity  of  1  m.  per  second  be  taken 
as  a  unit,  then  a  mass  of  5k.,  moving  with  the  same  velocity,  would  have 
5  units  of  momentum  ;  and  if  the  latter  mass  should  have  a  velocity  of 
10  m.  per  second,  its  momentum  would  be  5  X  10  =  50  units. 

27.  Newton's  Second  Law.  Change  of  momentum  is  in  the 
direction  in  which  the  force  acts,  and  is  proportional  to  its  inten- 
sity and  to  the  time  during  which  it  acts. 

This  law  (except  as  regards  direction)  is  expressed  in  the 
following  formula  :  m  v  =ft. 

The  product /£  is  called  the  impulse  of  the  force.     In  cer- 


SIR    ISAAC   NEWTON. 

[From  the  original  painting  by  Sir  Godfrey  Knotter.J 


NEWTON'S  SECOND  LAW.  29 

tain  cases,  such  as  that  of  a  blow  from  a  hammer,  it  is  quite 
impracticable  to  measure  either  the  force  or  the  (very  short) 
time  during  which  it  acts,  but  its  effect,  i.e.  the  change  of 
momentum,  can  be  measured. 

The  product /£  signifies  that  the  momentum  imparted  to  a 
body  is  proportional  to  the  time  (t~)  during  which  a  force  acts 
and  to  the  intensity  (/)  of  the  force.1  We  infer  from  this 
equation  that  a  definite  force  acting  upon  any  mass  for  a  given 
time  will  generate  in  it  a  velocity  which  is  inversely  proportional 
to  the  mass. 

This  law  declares,  by  implication,2  (1)  that  an  unbalanced 
(§  42)  force  in  a  given  time  always  produces  exactly  the  same 
change  of  momentum,  regardless  of  the  mass  of  the  body  /  that 
an  unbalanced  force  never  fails  to  produce  a  change  of  momen- 
tum j  hence  any  force,  however  small,  can  move  any  free  body, 
of  hoivever  great  mass. 

For  example,  a  child  can  move  a  body  having  a  mass  equal  to  that  of 
the  earth,  and  the  momentum  that  the  child  can  generate  in  this  immense 
body  in  a  given  time  is  precisely  the  same  as  that  which  he  would  gen- 
erate by  the  exertion  of  the  same  force  for  the  same  length  of  time  on  a 
body  having  a  mass  of  (say)  10  pounds.  Momentum  is  the  product  of 
mass  into  velocity  ;  so,  of  course,  as  the  mass  is  large,  the  velocity 
acquired  in  a  given  time  will  be  correspondingly  small.  The  instant  the 
child  begins  to  act  the  immense  body  begins  to  move.  Its  velocity, 
infinitesimally  small  at  the  beginning,  would  increase  at  an  almost  infini- 
teshnally  slow  rate,  so  that  it  might  be  years  before  its  motion  would 
become  perceptible.3 

1  This  formula  virttially  asserts  that  where  there  is  no  force  there  is  no  change  of 
momentum  (i.e.  if/  =  0,/£  =  0).    Hence,  Newton's  First  Law  is  a  corollary  to  the 
Second  Law. 

2  No  reference  is  made  in  the  law  to  the  mass  of  the  body  acted  upon. 

3  It  is  easy  to  see  how  persons  may  get  the  impression  that  very  large  masses  are 
immovable  except  by  very  great  forces.    The  erroneous  idea  is  acquired  that  bodies 
of  matter  are  capable  of  resisting  the  tendency  of  forces  to  cause  motion,  and  that  the 
greater  the  mass,  the  greater  the  resistance  ("  quality  of  not  yielding  to  force. "- 
WEBSTER).    The  fact  is,  that  no  body  of  whatever  mass  can  resist  motion;  in  other 
words,  "a  body  free  to  move  cannot  remain  at  rest  under  the  slightest  unb<tl<m<-«1 
force."  But  as  time  is  always  required  to  generate  change  of  momentum,  there  arises 
thence  a  deceptive  appearance  of  resistance  or  holding  back, 


30  MOLAK    DYNAMICS. 

This  law  declares,  by  implication,  (2)  that  a  force  acting  on 
a  body  in  motion  produces  just  the  same  effect  as  if  it  were 
acting  on  the  same  body  at  rest,  for  no  reference  is  made  in  the 
law  to  the  state  of  the  body  acted  upon. 

Experiment.  Draw  back  the  rod  d  (Fig.  19)  towards  the  left,  and 
place  the  detent  pin  c  in  one  of  the  slots.  -  Place  one  of  the  brass  balls 
on  the  projecting  rod,  and  in  contact  with  the  end  of  the  instrument,  as 
at  A.  Place  the  other  ball  in  the  short  tube  B.  Raise  the  apparatus  to 


\ 
\ 
\ 


\ 

\ 
\ 
\ 


1 

t  \ 


FIG.  19. 

as  great  an  elevation  as  practicable,  and  place  it  in  a  perfectly  horizontal 
position.  Release  the  detent,  and  the  rod,  propelled  by  the  elastic  force 
of  the  spring  within,  will  strike  the  ball  B,  projecting  it  in  a  horizontal 
direction.  At  the  same  instant  that  B  leaves  the  tube  and  is  free  to  fall, 
the  ball  A  is  released  from  the  rod  and  begins  to  fall.  The  sounds  made 
on  striking  the  floor  reach  the  ears  of  the  observer  at  the  same  instant ; 
this  shows  that  both  balls  reach  the  floor  in  sensibly  the  same  time,  and 
that  the  horizontal  motion  which  one  of  the  balls  has  does  not  affect  the 
time  of  its  fall,  i.e.  does  not  modify  the  effect  of  the  force  of  gravity.1 

1  This  principle  of  the  independence  of  simultaneously  acting  forces  was  an 
experimental  discovery  made  by  Galileo.  Before  his  time  it  was  held  that  one 
cause  must  cease  to  act  before  another  can  commence  to  do  so  ;  and,  accordingly,  it 
was  believed  that  when  a  projectile  Avas  shot  into  the  air  (instead  of  commencing  its 
fall  immediately),  the  force  of  projection  must  be  expended  before  any  tendency  to 
fall  could  assert  itself, 


ACTION    AND    RE  ACTION.  31 

The  law  implies  (3)  that  if  two  or  more  forces  act  on  a 
body,  each  produces  its  own  change  of  momentum  in  its  own 
direction,  independently  of  the  others. 

It  declares,  as  we  shall  see  later,  that  the  operation  of  compounding 
forces  is  just  the  same  as  that  of  compounding  the  motions  which  the 
several  forces  acting  simultaneously  tend  to  produce. 

28.  Pulls  and  Pushes ;  Action  and  Reaction.     Every  force 
is  either  a  pull  or  a  push,  and  is  accordingly  called  an  attract- 
ive or  a  repellent  force.     It  is  evident  that  there  can  be  no  pull 
or  push  except  between  at  least  two  bodies  or  two  parts  of  the 
same  body ;  i.e.  there  is  no  such  thing  as  a  one-sided  pull.     It 
is  not  possible  for  a  person  to  pull  without  being  himself 
pulled,  or  to  push  without  being  himself  pushed. 

Appearances  sometimes  seem  to  contradict  the  above  statements.  For 
example,  a  man  standing  on  a  wharf  pulls  a  distant  boat  by  means  of  a 
rope.  The  boat  moves  as  the  result  of  the  pull,  but,  though  he  is  bracing 
himself  against  the  wharf,  he  is  not  willing,  perhaps,  to  concede  that  he 
is  likewise  pulled.  Let  him  stand  in  the  boat  and  pull  the  rope  which  is 
attached  at  the  other  end  to  the  wharf;  both  he  and  the  boat  move. 
What  body,  according  to  appearances,  is  pulled  in  this  case  ?  What 
bodies  are  actually  pulled  ? 

Force  is  always  dual,  inasmuch  as  it  is  always  oppositely  directed  upon 
two  bodies.  By  a  conventionality  of  speech  we  say  that  one  of  the  two 
bodies  acts  upon  the  other,  and  the  latter  reacts  upon  the  former. 

The  wings  of  a  bird  act  upon  the  air,  giving  a  certain  portion  of  it  a 
rearward  motion ;  the  air  reacts  upon  the  wings,  giving  the  bird  a  for- 
ward motion.  The  bat  strikes  the  ball,  imparting  to  it  an  acceleration; 
the  ball  reacts  upon  the  bat,  giving  it  a  negative  acceleration. 

29.  Newton's  Third  Law.     To  every  action  there  is  an  equal 
and  opposite  reaction. 

If  action  and  reaction  were  not  equal  there  might  be  a  possibility  that 
a  person  might  raise  himself  by  pulling  on  the  soles  of  his  feet  or  the  hair 
of  his  head ;  that  a  vessel  might  be  propelled  in  a  calm  by  blowing  against 
its  sail  with  a  powerful  bellows  (operated  by  steam)  located  on  the  deck 
of  the  same  vessel ;  that  a  person  sitting  in  a  buggy  might  give  himself  a 
ride  by  pressing  his  feet  against  the  dasher  ;  that  a  person  might  advance, 


32  MOLAR    DYNAMICS. 

i.e.  move  his  center  of  mass,  without  having  the  earth  beneath  him ;  or 
that  a  bird  might  fly  without  having  the  external  air  to  act  upon. 

In  case  of  an  action  between  two  bodies  that  are  free  from 
the  action  of  resisting  forces,  the  law  implies  that  the  mo- 
menta generated  by  the  action  and  by  the  reaction  are  equal. 
The  recoil  of  a  rifle  affords  a  good  illustration  of  this.  The 
explosion  of  the  powder  inside  the  barrel  exerts  equal  and 
opposite  impulses  on  the  ball  and  on  the  gun,  and  causes  them 
to  move  in  opposite  directions  with  equal  momenta.  Hence, 
if  the  speed  of  the  recoil  of  the  rifle  be  known,  the  speed  of 
the  ball  can  be  computed,  and  vice  versa. 

For  example,  let  the  masses  of  the  rifle  and  the  ball  be  respectively  5  Ib. 
and  1  oz.,  and  the  maximum  velocity  of  the  rifle  be  10  feet  per  second. 
Then  the  momentum  of  the  rifle  at  the  instant  is  (5  X  10  =  )  50  units. 
But  the  momentum  of  the  ball  at  the  same  instant  is  also  50  units.  Hence, 
(50  -r  j1^  — )  800  feet  per  second  is  the  maximum  velocity  of  the  ball. 

EXERCISES. 

1.  How  are  we  made  aware  of  the  existence  of  force  ? 

2.  A  10-lb.  ball  rests  upon  a  table,     (a)  How  great  an  upward  pres- 
sure does  the  table  exert  upon  the  ball  ?     (6)  How  do  you  explain  this 
pressure  ? 

3.  Is  perpetual  motion  possible  ? 

4.  A  carriage  is  suddenly  stopped,  and  the  passengers  are  said  to  be 
"  thrown  out."     Are  they  thrown  ? 

5.  What  is  a  suitable  name  to  apply  to  all  interaction  between  bodies  ? 

6.  (a)  Why  may  a  man  raise  himself  by  pulling  on  a  horizontal  bar, 
but  not  by  pulling  on  any  part  of  his  person  ?     (b)  In  which  case  is  he 
acted  upon  by  an  external  force  ?     (c)  In  the  first  case,  which  body 
receives  the  action  and  which  the  reaction  ?     (d)  State  what  receives  the 
action  in  the  second  case,  and  what  receives  the  reaction. 

7.  When  do  action  and  reaction  neutralize  each  other  and  have  no 
tendency  to  produce  a  change  of  motion  ? 

8.  What  agent  is  the  immediate  cause  of  motion  ? 

9.  What  distinction  do  you  make  between  velocity  and  momentum  ? 
10.    Upon  what  does  the  momentum  given  to  a  ball  fired  from  a  gun 

by  the  expanding  gases  depend  ? 


EXERCISES.  33 

11.  Inasmuch  as  equal  forces  are  exerted  for  the  same  length  of  time 
by  the  gases  on  the  ball  and  the  gun,  how  will  the  momenta  communi- 
cated to  the  two  compare  ? 

12.  If  there  be  25  Ibs.  of  matter  in  the  gun  and  1  oz.  (T^  Ib.)  in  the 
ball,  and  the  gun  acquire  a  maximum  velocity  of  3  feet  per  second,  what, 
at  that  instant,  is  the  velocity  of  the  ball  ? 

13.  Can  any  body  be  put  in  motion  in  no  time  ?    (Demonstrate  from 
formula  Ft  =  M  V.) 

14.  Compare   the  momentum  of  a  car  weighing  50  tons,  moving  10 
feet  per  minute,  with  that  of  a  lump  of  ice  weighing  5  cwt. ,  at  the  end 
of  the  third  second  of  its  fall. 

15.  With  what  velocity  must  a  boy  weighing  25  k.  move  to  have  the 
same  momentum  that  a  man  weighing  80  k.  has  when  running  at  the  rate 
of  10  km.  per  hour? 

16.  Since  F  t  =  M  F,  to  what  is  change  of  momentum  proportional  ? 

17.  If  the  same  force  act  for  the  same  length  of  time  upon  bodies  hav- 
ing different  masses,  to  what  will  the  velocities  produced  be  proportional  ? 

18.  Two  boats  of  unequal  masses  are  brought  together  by  pulling  on 
a  rope,    (a)  Eesistance  being  disregarded,  how  will  their  momenta  at  any 
given  instant  compare  ?    (6)  How  will  their  velocities  at  the  same  instants 
compare  ? 

19.  If  the  motion  of  the  moon  in  its  orbit  about  the  earth  were  to 
cease,  these  bodies  would  approach  each  other.     The  mass  of  the  earth 
is  about  80  times  that  of  the  moon.     What  part  of  the  whole  distance 
between  them  would  the  moon  move  before  collision  ? 

20.  (a)  Why  does  not  a  given  force,  acting  the  same  length  of  time, 
give  a  loaded  car  as  great  a  velocity  as  an  empty  car  ?     (6)  After  equal 
forces  have  acted  for  the  same  length  of  time  upon  both  cars,  and  have 
given  them  unequal  velocities,  which  will  be  the  more  difficult  to  stop  ? 

21.  (a)  The  planets  move  unceasingly  ;  is  this  evidence  that  there  are 
forces  pushing  or  pulling  them  along  ?     (6)  None  of  their  motions  are  in 
straight  lines  ;  are  they  acted  upon  by  external  forces  ? 

22.  A  certain  body  is  in  motion.      Suppose  that  all  hindrances  to 
motion  and  all  external  forces  be  withdrawn   from  it,  how  long  will 
it  move  ?      Why  ?      In  what  direction  ?      Why  ?     With  what  kind  of 
motion,  i.e.  accelerated,  retarded,  or  uniform?     Why? 

23.  If  one  body  have  four  times  the  mass  of  another,  how  must  the 
forces  applied  to  them  compare  in  order  to  give  them  equal  momenta  in 
equal  times  ? 


34  MOLAK  DYNAMICS. 

SECTION  III. 
MEASUREMENT  OF  FORCE. 

30.  Weight.  Gravitation  Units  of  Force.  We  have  here  to 
anticipate  what  will  hereafter  be  more  fully  discussed,  by 
defining  the  weight  of  any  given  mass  as  the  measure  of  the 
force  of  gravity  which  exists  between  it  and  the 
earth.  Weight  is  a  force.  Its  magnitude  is  usually 
determined  by  measuring  the  strain  (§  23)  which  it 
produces  in  the  supporting  body,  e.g.  the  elongation 
of  the  spring  in  a  spring  balance. 


The  household   instrument   called    a   spring  balance   is, 
strictly  speaking,  a  dynamometer,  i.e.  a  force-measurer.     It 
contains  a  spiral  spring,  as  seen  in  A  (Fig.  20),  carrying  an 
index  which  moves  over  a  scale,  as  shown  in  B.     If  a  unit 
FIG.  20.     mass  (e.g.  1  Ib.  or  1  k.)  be  hung  upon  the  spring,  the  latter 
is  lengthened  by  a  certain  definite  quantity.    If,  grasping  the 
ring  in  one  hand  and  the  hook  in  the  other,  you  lengthen  the  spring  by  a 
muscular  pull  as  much  as  it  was  lengthened  by  the  force  of  gravity  acting 
on  the  mass,  the  inference  is  that  the  muscular  force  which  you  exert 
is  equal  to  the  force  of  gravity  exerted  on  the  mass. 

The  units  generally  employed  in  measuring  force  are  the 
pound  and  the  kilogram,  and  are  called  the  gravitation  units. 

All  forces  may  be  measured  in  the  same  units.  To  say  that 
a  man  pulls  a  boat  with  a  force  of  one  hundred  pounds  is 
equivalent  to  saying  that  he  pulls  with  a  force  that  is  equal 
to  the  force  which  acts  between  the  earth  and  a  body  having 
a  mass  of  one  hundred  pounds.  A  force  of  one  pound,  then, 
is  an  abbreviated  expression  for  a  force  equal  to  the  weight 
(at  the  locality  in  question)  of  a  mass  of  one  pound.  The 
pound  and  the  kilogram  are  primarily  units  of  mass. 

31.  Force  Tends  to  Produce  Acceleration.  A  constant  force 
acting  upon  a  free  body  always  produces  uniformly  accelerated 
motion.  This  is  best  illustrated  by  the  fall  or  ascent  of  a 
body  in  a  vacuum,  the  body  being  meantime  acted  on  only 


MEASUREMENT    OF    FORCE.  35 

by  the  constant  force  of  gravity.  In  its  ascent  the  force  of 
gravity  causes  a  uniform  negative  acceleration ;  in  its  fall  it 
causes  a  uniform  positive  acceleration. 

32,  Measurement  of  Force  by  Direct  Observation  of  Acceler- 
ation and  Mass,     If  a  force,  /,  be  applied  to  a  certain  mass, 
m,  for  a  unit  of  time,  a  certain  momentum  is  generated  in  the 
mass.     If  the  same  force  be  applied  to  a  greater  mass  for  the 
same  time,  it  will  move  with  as  many  times  less  velocity  as 
the  mass  is  times  greater,  but  the  product  of  the  mass  and  the 
velocity,  i.e.  the  momentum,  is  the  same.     That  is,  the  same 
force  acting  for  the  same  length  of  time  on  free  bodies  having 
different  masses  may  be  measured  by  the  change  of  momentum 
generated  by  it  in  a  unit  of  time  (e.g.  a  second),  since  this  is 
constant  and   depends  on  nothing  but  the  force.      That  is, 
/=  m  a,  in  which  /  represents  any  constant  force  acting  on 
any  mass  m,  a  the  acceleration,  and  ma  the  rate  of  change  of 
momentum.1 

33,  Fundamental  Units.    A  system  of  units  can  be  built  on 
any  selected  units  of  length,  mass,  and  time.     All  so-called 
dynamical  units  can  be  derived  from  these ;  hence,  these  are 
called  fundamental  units.     Thus,  a  system  of  units  derived 
from  the  centimeter  (unit  of  length),  the  gram  (unit  of  mass), 
and  the  second  (unit  of  time),  is  called  the  centimeter-gram- 
second  system,  written  the  C.  G.  S.  system. 

34,  C,  G.  S.  Absolute  Units  of  Force.     The  dynamical  unit 
of  force  is  that  force  which  will  impart  to  a  unit  mass  a  unit 
acceleration. 

The  unit  of  force  in  the  C.  Gr.  S.  system  is  called  a  dyne,  and 
is  that  force  which  is  capable  of  giving  to  a  gram  mass  an 
acceleration  of  one  centimeter  per  second /  in  other  words,  it  is 
a  constant  force  of  the  requisite  intensity  to  impart  in  one 

1  Many  physicists  do  not  treat  force  as  a  cause  (§  22),  but  as  a  phenomenon,  and 
define  it  as  the  time  rate  of  change  of  momentum. 


36  MOLAR    DYNAMICS. 

second  to  a  gram-mass  a  velocity  of  one  centimeter  per  second. 
Any  force  may  be  measured  in  dynes,  and  a  spring  balance 
might  be  graduated  in  dynes  so  as  to  measure  force  in  abso- 
lute units. 

It  is  important  to  observe  that  the  dynamical  units  of  force 
are  absolute;1  i.e.  unlike  the  gravitation  units  of  force,  they 
are  not  affected  by  variations  in  the  force  of  gravity,  and  are 
therefore  everywhere  the  same.2 

A  dyne  is  a  very  small  force.  In  expressing  force  of  considerable 
magnitude  the  megadyne  (a  million  dynes)  is  commonly  used.  A  mega- 
dyne  is  rather  more  than  the  force  of  a  kilogram. 

35.  British  Absolute  Units.     Corresponding  to  the  metric  C.  G.  S. 
system  is  the  British  Foot  round  Second  (F.  P.  S.)  system.     The  British 
absolute  unit  of  force  is  the  poundal.     A  poundal  is  that  force  which  is 
capable  of  giving  to  a  pound-mass  an  acceleration  of  one  foot  per  second. 

36.  Expression  for  Weight  in  Absolute  Units,      Any   con- 
stant force  which  in  one  second  produces  in  a  mass  of  m  grams 
an  acceleration  of  a  centimeters  per  second  must  be  equal  to 
mXa  dynes   (i.e.  f=ma).     The  letter  g  is  generally  used 
instead  of  the  letter  a  to  denote  the  acceleration  due  to  the 
force  of  gravity.     By  exact  measurement  the  acceleration  pro- 
duced by  the  force  of  gravity  on  all  free  bodies  (i.e.  in  a  vac- 
uum) is  found  to  be,  in  the  latitude  of  Boston  at  the  level  of 
the  sea,  980.4  cm.   (or  nearly  32.2  feet)  per  second.     Hence, 
the  force  of  gravity  acting  on  a  mass  of  one  gram  must  be 
(substituting,  in  the  equation  above,  w  (weight)  for  /,  and  g 
for  a)  w  —  mg  =  1  X  980.4  =  980.4  dynes.     Consequently,  it 
requires  a  force  of  980.4  dynes  to  support  (i.e.  prevent  from 
falling)  a  mass  of  one  gram ;  or  the  weight  of  a  gram-mass  at 
sea  level  in  latitude  42°  is  980.4  dynes.3     A  dyne  is  therefore 

1  The  dynamical  system  of  units  is  frequently  called  the  absolute  system. 

2  The  relation  expressed  in  the  formula  f=m a  is  based  on  the  supposition  that 
the  unit  of  force  is  the  dynamical  unit.    When  measured  in  gravitation  units,/  is  not 
equal  to,  hut  only  proportional  to,  ma. 

3  The  equation  w  =  mg  expresses  the  fact  that  (using  C.  G.  S.  units)  the  number 
of  dynes  which  a  given  mass  weighs  is  g  times  the  number  of  grams  in  that  mass. 


EXPRESSION    FOB    MASS.  37 

about  5-|o  of  the  weight  of  a  gram-mass,  or  more  exactly  ^^.F 
of  the  weight  of  a  gram-mass  at  Paris.  In  the  gravitation  sys- 
tem the  weight  of  a  gram-mass  is  a  gram-force;  hence,  1  gram- 
force  =  980.9  dynes  at  Paris.  Gravitation  units  in  grams- 
force  at  Paris  are  readily  changed  into  dynes  by  multiplying 
by  980.9  ;  at  Boston,  by  multiplying  by  980.4  ;  and  generally 
by  multiplying  by  the  value  of  g  at  any  place.1 

37.  Expression  for  the  Mass  of  a  Body  in  Terms  of  its 

Weight.     Since  w  =  m  g,  m  —  —\  that  is,  mass  is  measured 

y 

by  its  weight  in  dynes  or  poundals,  divided  by  the  accelera- 
tion in  centimeters  or  feet  per  second  produced  by  gravity. 
Although  w  and  g  vary  with  location  (§  66),  they  vary  pro- 

w 
portionally;  hence,  the  ratio  —  (i.e.  the  mass)  does  not  change, 

but  is  constant  for  the  same  body. 

38.  Problems  and  Solutions.     A  body  suspended  from  a  spring 
balance  is  found  to  weigh  at  Paris  %  k.     Required  its  weight  in  dynes. 
Solution:   |  k.  =  500  g. :  500  X  980.9  =  490,450  dynes. 

Required  to  find  the  force  which,  acting  for  10  seconds,  gave  to  a  mass 
of  10  g.  a  velocity  of  1000  cm.  per  second.     Solution: 

F=™  =  10X^0  =  1000  dynes. 

Required  to  find  the  mass  in  which  a  force  of  1500  dynes  produces  an 

•p<     -t  /^oo 

acceleration  of  2  cm.  per  second.     Solution:  m  =  -  =  —  —  =  750  g. 

ct        ^ 

Required  to  find  the  acceleration  which  a  force  of  2000  dynes  can  give 

W       2000 

a  mass  of  4  g.     Solution:  a  —  — =  500  cm.  per  second. 

m        4 

39.  Two  Systems  of  Measurement  of  Force.  We  have  found 
in  the  foregoing  discussions  that  there  are  two  methods  of 
measuring  force  :  one  specially  adapted  to  measuring  balanced 
forces  (see  p.  41),  called  the  statical  or  gravitation  system  ;  the 
other  specially  adapted  to  measuring  unbalanced  forces  (see 

1  The  weight  of  a  pound-mass  is  equal  to  32.2  poundals  ;  or  the  poundal  as  a  unit 
of  force  is  3^.3  of  a  pound-force  or  nearly  equal  to  the  weight  of  half  an  ounce. 


38 


MOLAR   DYNAMICS. 


p.  42),  called  the  dynamical  or  absolute  system  ;  though  a  force, 
whether  balanced  or  unbalanced,  may  always  be  measured  by 
either  system.  The  gravitation  system  is  so  called  because 
by  it  forces  are  compared  with  the  force  of  gravity  as  a  stand- 
ard. The  two  methods  of  measuring  force  give  rise  to  two 
systems  of  units,  called  respectively  the  gravitation  and  the 
absolute  systems,  either  one  of  which  is  easily  convertible  into 
the  other. 

40.  Galileo's  Experiment.  Galileo  let  fall  from  the  lean- 
ing tower  at  Pisa *  iron  balls  of  different  masses,  and  found 
that  they  fell  with  equal  acceleration  and  reached  the  ground 
at  the  same  instant.  This  celebrated 
experiment  established  two  impor- 
tant facts  : 

(1)  At  any  given  place  the  acceler- 
ation due  to  gravitation  is  independ- 
ent of  the  mass  of  the  falling  body. 

This  fact  may  also  be  deduced 
from  the  formula  f=ma.  For,  if  f 
be  proportional  to  m,  it  follows  that 
a  must  be  the  same  for  all  bodies. 
That  the  force  of  gravity  /  is  pro- 
portional to  mass  m  at  the  same 
place  was  demonstrated  by  Galileo's 
experiment.  For,  let  /  and  /'  be 
the  intensities  of  two  forces  drawing 
two  bodies,  whose  masses  are  respec- 
tively m  and  m',  to  the  earth ;  then 

f=  ma,  and/'  =  m'  a'; 
but,  as  proved  by  Galileo's  experiment, 

a  =  a' : 


FIG.  21. 


1  Tliis  building  (Fig.  21),  consisting  of  a  series  of  open  galleries  one  above  another 
reaching  to  a  total  hight  of  179  feet,  is  admirably  adapted  to  the  purpose  here  stated. 


GALILEO. 


OF  THE 

UNIVERSITY 

OF 


GALILEO'S   EXPERIMENT. 


39 


f       m 
hence  (dividing),  '—  =  — , 

and,  in  general,  f  co  m  ; 

i.e.  (2)  £Ae  intensity  of  the  earth's  attraction  at  the  same 
place  varies  as  the  mass. 

In  other  words,  the  deductions  from  this  experiment 
are :  (1)  that  all  free  bodies,  whatever  their  mass,  fall 
toward  the  earth  with  equal  accelerations ;  and  (2) 
that  if  one  body  possess  twice  the  mass  of  another, 
twice  the  force  is  required  to  give  it  the  same  acceler- 
ation. 

Proposition  (1)  is  seemingly  contradicted  by  everyday  expe- 
rience, for  if  a  coin  and  a  piece  of  tissue  paper  be  dropped  from 
a  hight  they  fall  with  very  different  velocities.  But  if  a  coin 
and  a  feather  be  placed  in  a  long  glass  tube  (Fig.  22),  the  air 
exhausted,  and  the  tube  turned  end  for  end,  it  will  be  found 
that  the  coin  and  the  feather  fall"  in  the  vacuum  with  equal 
velocities.  It  is  evident,  then,  that  when  there  is  a  difference 
in  the  acceleration  of  falling  bodies  at  the  same  place  it  is  not  due  to 
the  force  of  gravitation,  but  to  some  other  force:  e.g.  the  resistance  of 
the  air. 


FIG.  22. 


EXERCISES. 

1.  Define  a  gravitation  unit  of  force  and  an  absolute  unit  of  force, 
and  state  wherein  the  latter  for  scientific  purposes  is  preferable  to  the 
former. 

2.  A  constant  force   acting  on  a  free  body  produces  what  kind  of 
motion  ? 

3.  Explain  the  meaning  of  the  equation  w  =  mg. 

4.  To  what   is  the   acceleration  produced  in  equal  masses  propor- 
tional, —  i.e.  if  m  is  constant,  a  will  vary  as  what  ? 

5.  On  what  condition  will  equal  forces  produce  equal  accelerations  ? 

6.  Suppose  that  you  fill  a  box  with  sand,  place  it  on  a  toy  cart,  pull 
the  cart  by  a  string  with  a  constant  force  along  a  smooth  floor  for  a  cer- 
tain number  of  seconds,  and  observe  the  acceleration  given  the  load 
(cart,  box,  and  sand),  then  remove  the  sand  and  replace  it  with  lead  shot. 


40  MOLAR   DYNAMICS. 

How  can  you  tell,  by  pulling  the  load  with  the  same  force  as  before, 
when  it  has  the  same  mass  as  the  former  load  ? 

7.  (a)  Has  the  same  mass  equal  weights  in  Paris  and  Boston  ?  (6)  How 
sensitive  must  a  spring  balance  be  to  discover  any  difference  ? 

8.  (a)  When  we  speak  of  a  force  of  one  pound,  what  do  we  mean  ? 
(6)  When  we  speak  of  a  force  of  one  dyne,  what  do  we  mean  ?  (c)  When 
we  speak  of  a  mass  of  one  pound,  what  do  we  mean  ? 

9.  (a)  If  one  mass  be  four  times  another,  how  many  times  as  much 
force  is  necessary  to  produce  the  same  acceleration  in  the  former  as  in 
the  latter  ?    (6)  How  many  times  greater  is  the  force  of  gravity  acting  on 
a  mass  of  one  hundred  pounds  than  on  a  mass  of  one  pound  ?     (c)  If  a 
hundred-pound  iron  ball  and  a  one-pound  iron  ball  be  let  drop  from  the 
same  hight  at  the  same  instant,  which  ought  to  reach  the  ground  first  ? 

10.  A  body  weighing  4  g.  is  moving  with  an  acceleration  of  12  cm.  per 
second.     What  is  the  force  acting  ? 

11.  A  body  acted  on  by  a  force  of  100  dynes  receives  an  acceleration 
of  20  cm.  per  second.     What  is  its  mass  ? 

12.  A  body  of  mass  30  g.  is  moved  by  a  constant  force  of  50  dynes. 
What  is  its  acceleration  ? 

13.  What  acceleration  will  a  force  of  20  dynes  produce  on  a  mass  of 
10  g.? 

14.  What  velocity  will  a  force  of  20  dynes  acting  on  1  k.  impart  to  it 
in  5  minutes  ? 

15.  (a)  What  is  the  weight  in  dynes  of  a  mass  of  1  k.  in  Boston  ? 
(b)  How  many  more  dynes  does  it  weigh  in  Paris  ? 

16.  A  constant  force  of  20  dynes  acts  on  a  mass  of  5  g.  and  gives  it  a 
velocity  of  500  cm.  per  second.     How  many  seconds  does  it  act  ? 

17.  How  is  the  value  in  dynes  of  a  gram  weight  at  any  locality  deter- 
mined ? 

18.  How  many  times  greater  is  the  static  unit  of  force  (one  gram) 
than  the  dynamic  unit  ? 

19.  A  man  jumps  from  an  elevation  with  a  50-pound  weight  in  his 
hand.     What  is  the  pressure  of  the  weight   on   his   hand   during  his 
descent  ? 

20.  How  far  can  a  force  of  10  dynes  move  a  kilogram  mass  in  a  minute  ? 

Solution:  /=  ma,  or  10  =  1000  a  ;  whence  a=  .01  cm.  per  second. 
Distance  traversed  from  rest  in  one  minute  =  %  a  t'2  =  '—  X  GO2  =  18  cm. 


GRAPHICAL    REPRESENTATION    OF    FORCE.  41 

SECTION   IV. 
COMPOSITION   AND   RESOLUTION   OF   FORCES. 

41,  Graphical  Representation  of  Force.     A    force    is    de- 
fined when  its  magnitude,  direction,  and  point  of  application 
are  given.     We  may  represent  forces  graphically  by  straight 
lines  whose  lengths   bear  to  one  another  the  same  relation 
as  the  numerics  of  the  forces,  while  the  directions  of  these 
lines   indicate  the  directions    of   the  forces,  and  the  points 
from    which    the    lines    are    drawn    indicate    the   points   of 

application.     Thus,  on  a   scale  of    A > B 

1   cm.  =  1  k.  the  line  A  B  (Fig.  23)     Q , £ 

represents  a  force  of  3.2  k.   acting  FIG.  23. 

toward  the  right  with  its  point  of  application  at  A  ;  and  the 
line  D  E  represents  a  force  of  2  k.  acting  parallel  to  the  first, 
with  its  point  of  application  at  D. 

42.  Composition  of  Forces  Acting  in  the  Same  Line;  Equi- 
librium of  Forces;  Balanced  Forces. 

Experiment.  Insert  two  stout  screw-eyes  into  the  opposite  ex- 
tremities of  a  block  of  wood.  Attach  a  spring  balance  to  each  eye. 
Let  two  persons  pull  on  the  spring  balances  at  the  same  time,  and  with 
equal  force,  as  shown  by  the  indexes,  but  in  opposite  directions.  The 
block  does  not  move.  One  force  just  neutralizes  the  other,  and  the 
result,  so  far  as  any  movement  of  the  block  is  concerned,  is  the  same  as 
if  no  force  acted  on  it. 

When  one  force  opposes  in  any  degree  another  force,  each 
is  spoken  of  as  a  resistance  to  the  other.  Let  f  represent  the 
number  of  pounds  of  any  given  force,  and  let  a  force  acting 
in  any  given  direction  be  called  positive,  and  indicated  by  the 
plus  (+)  sign,  and  a  force  acting  in  an  opposite  direction 
to  the  force  which  we  have  denominated  positive  be  called 
negative,  and  indicated  by  the  minus  (— )  sign.  Then  if  two 
forces,  -f-/  and  —  f,  acting  on  a  body  at  the  same  point  or 
along  the  same  line  be  equal,  they  are  said  to  be  balanced, 
and  the  result  is  that  no  change  of  motion  is  produced. 


42  MOLAR    DYNAMICS. 

Viewed  algebraically,  +  /  —  f=  0  ;  or,  correctly  interpreted, 
+  /  —  /=<>=  (is  equivalent  to)  0,  i.e.  no  force.  In  all  such 
cases  there  is  said  to  be  an  equilibrium  of  forces,  and  the 
body  is  said  to  be  in  a  state  of  equilibrium.  Equilibrium 
is  the  condition  of  two  or  more  forces  which  are  so  opposed 
that  their  combined  action  on  a  body  produces  no  change  in 
its  rest  or  motion. 

A  force  that  produces  equilibrium  with  one  or  more  forces 
is  called  an  equilibrant.  That  branch  of  dynamics  which 
treats  of  the  relation  of  force  to  the  motion  which  it  produces 
is  called  kinetics,  and  that  branch  which  treats  of  equilibrium 
of  forces  is  called  statics. 

43.  Unbalanced  Forces.  If  one  of  the  forces  be  greater 
than  the  other,  the  excess  is  spoken  of  as  an  unbalanced  force, 
and  its  direction  is  indicated  by  one  or  the  other  sign,  as  the 
case  may  be.  Thus,  if  a  force  of  +  8  Ibs.  act  on  a  body 
toward  the  east,  and  a  force  of  —  10  Ibs.  act  on  the  same 
body  along  the  same  line,  then  the  unbalanced  force  is  —  2 
Ibs. ;  i.e.  the  result  is  the  same  as  if  a  single  force  of  2  Ibs. 
acted  on  the  body  toward  the  west.  Such  an  equivalent  force 
is  called  a  resultant.  A  resultant  force  is  a  single  force  that 
may  be  substituted  for  two  or  more  forces  and  produce  the  same 
result  that  the  simultaneous  action  of  the  several  forces  would 
produce. 

The  resultant  of  any  number  of  forces  acting  in  the  same  straight  - 
line  is  equal  to  the  algebraic  sum  of  the  forces.  An  equilibrant 
of  several  forces  is  equal  in  magnitude  to  their  resultant,  but 
opposite  in  direction.  The  process  of  combining  several  forces 
so  as  to  find  their  resultant  is  called  composition  of  forces. 
The  forces  combined  are  called  components.  The  converse 
operation,  of  finding  component  forces  which  shall  have  the 
same  effect  as  a  given  force,  is  called  resolution  of  forces. 

An  unbalanced  force  always  produces  acceleration.  Hence,  a 
body  acted  on  by  an  unbalanced  force  cannot  be  at  rest. 


PRESSURE,    TENSION.  43 

44,  Pressure;  Tension.  A  balanced  force  does  not  pro- 
duce acceleration,  but  causes  either  a  pressure  or  a  tension. 
A  force  exerts  pressure  when  it  tends  to  compress  or  shorten 
in  the  direction  of  its  action  the  body  on  which  it  acts. 
Examples  :  pressure  exerted  on  the  springs  of  a  carriage, 
on  air  when  it  is  compressed  in  an  air  gun,  etc.  A  force 
;auses  tension  when  it  tends  to  lengthen  in  the  direction  of 
its  action  a  body  on  which  it  acts.  A  body  thus  subjected 
to  a  force  tending  to  elongate  it  is  said  to  be  in  a  state  of 
tension,  the  stress  to  which  it  is  subjected  is  called  its  tension, 
and  its  strength  to  resist  being  pulled  apart  is  called  its  tensile 
strength. 

Equilibrium  is  often  maintained  by  the  reaction  of  a  surface  with 
which  the  body  acted  on  is  in  contact.  A  simple  illustration  is  that  of 
a  body  supported  on  a  horizontal  surface,  as  that  of  a  table.  Here  the 
reaction  caused  by  the  compression  of  the  material  of  which  the  table 
is  composed  is  equal  to  the  weight  of  the  body. 

EXERCISES. 

1.  Explain  the  use  of  a  line  to^represent  a  force. 

2.  (a)  When  a  force  of  100  Ibs.  is  represented  by  a  line  5  in.  long, 
what  is  the  scale  ?     (6)    What  force  will  a  line  \  in.  long  represent  on 
the  same  scale  ? 

3.  (a)  Represent  on  a  scale  of  %  in.  =  1  Ib.  the  resultant  of  forces 
of  5  Ibs.  and  7  Ibs.  acting  in  the  same  direction.     (Always  place  arrow- 
heads in  lines  representing  forces  to  indicate  the  direction  of  the  forces.) 
(6)  Show,  by  points  A,  B,  and  C  placed  in  the  line,  the  components  of 
this  resultant.  •  (c)  Represent  the  same  two  forces  acting  in  opposite 
directions  upon  the  same  point  A.     (d)  How  will  you  represent  the 
resultant  of  these  two  opposing  forces  ? 

4.  Three  men,  A,  B,  and  C,  pull  on  a  rope  in  the  same  direction  with 
forces,  respectively,  of  50  Ibs. ,  60  Ibs. ,  and  70  Ibs.    A  is  nearest  the  end 
of  the  rope,  B  next,  and  C  next,     (a)  What  is  the  tension  of  the  rope 
between  A  and  B  ?     (b)  What  between  B  and  C  ?     (c)  A  man,  D,  just 
beyond  C  pulls  with  a  force  of  75  Ibs.  in  the  opposite  direction.     With 
what  force   must  a  man,    E,   pull,   that  there   may  be  equilibrium  ? 
(d)  When  there  is  equilibrium,  what  is  the  tension  of  the  rope  between 


44  MOLAR   DYNAMICS. 

C  and  D?  (e)  How  great  must  be  the  tensile  strength  of  the  rope 
between  C  and  D  ?  (/)  Write  the  equation  showing  the  algebraic 
addition  of  the  forces  in  case  of  equilibrium. 

5.  The  hooks  of  two  spring  balances  are  connected  by  a  string  and 
the  balances  are  pulled,     (a)  If  one  registers  5  Ibs.,  what  does  the  other 
register  ?     (6)  What  is  the  tension  in  the  string  ? 

6.  How  is  change  of  motion  produced  ? 

7.  What  other  effects  besides  change  of  motion  may  a  force  produce  ? 


SECTION   V. 

COMPOSITION    OF    PARALLEL   FORCES.       MOMENTS 
OF    FORCES. 

45.  Composition   of   Parallel   Forces  Acting  in  the  Same 
Direction  and  in  the  Same  Plane. 

Experiment.  A  B  (Fig.  24) 
represents  a  rod  in  a  horizonta 
position  with  three  strings  loosely 
looped  around  it  so  that  they  may 
be  slid  along  the  rod.  Dynamom- 

O^LJ^LJ-IO  eters  are  attached  to  the  free  ends 

of  the  strings.     The  strings  are  all 
stretched  in  parallel  directions  in  a 
plane  parallel   to   the   top  of  the 
FlG-  ^  table.     (Great  care  must  be  taken 


in  the  manipulation  to  keep  the  three  strings  exactly  parallel.)  The 
dynamometers  register  the  tensions  in  the  several  strings,  i.e.  the  forces 
applied  through  them  to  the  rod. 

Observe :  (I)  When  there  is  equilibrium  the  dynamom- 
eter E  registers  as  much  as  do  F  and  G  added  together. 
But  the  force  applied  at  C  is  the  equilibrant  of  the  other 
forces,  and  this  is  equal  to  their  resultant  acting  in  the 
direction  C  D.  (II)  The  point  of  application  of  the  resultant 
(or  equilibrant)  is  between  the  points  of  application  of  the 
components.  (HI)  This  point  is  nearer  the  greater  force. 
(IV)  The  distance  of  this  point  from  the  smaller  force  is  as 


DYNAMICAL   COUPLE.  45 

many  times  greater  than  its  distance  from  the  larger  force  as 
the  larger  force  is  times  the  smaller  force.  For  example,  if 
A  F  be  14  Ibs.  and  B  G  be  6  Ibs.  (14  :  6  =  7  :  3),  then  distances 
C  A  and  C  B  will  be  as  3  :  7.  In  other  words,  the  component 
forces  are  said  to  vary  inversely  as,  or  to  be  inversely  pro- 
portional to,1  their  distances  from  their  resultant.  These 
observations  are  summarized  as  follows  :  The  resultant  of 
two  parallel  forces  in  the  same  direction  is  equal  to  their  sum, 
and  the  distances  of  their  points  of  application  from  the  point 
of  application  of  the  resultant  vary  inversely  as  the  intensities 
of  the  components. 

Corollary  :  The  condition  of  equilibrium  is  that  the  algebraic 
sum  of  the  forces  (positive  and  negative)  must  be  zero. 

When  more  than  two  forces  act  on  a  body  in  the  same 
plane  and  in  the  same  direction,  the  resultant  of  any  two  of 
them  (and  its  point  of  application)  is  found,  then  the  result- 
ant of  this  resultant  and  a  third  force,  and  so  on  until  all 
have  been  used. 

46.  Dynamical  Couple.     Two   equal  forces  applied  to  the 
same  body  in  parallel  and  opposite  directions  not  in  the  same 
line  constitute  what  is   called  "  a  couple."     The  effect  of  a 
couple  is  to  produce  rotation,  but  no  motion  of  translation. 

Since  the  two  forces  which  constitute  a  couple  are  equal 
and  opposite,  their  resultant  is  zero,  and  therefore  no  single 
force  can  equilibrate  a  couple. 

47.  Moment  of   a     A        2ft.        C  8ft. 
Force.     The  value   of 


a  force  for  producing 

rotation  about  a  given 

,,    ,  .,  FIG.  25. 

axis  is  called  its  moment 

with  reference  to  that  axis.     Point  C  (Fig.  25)  may  represent 

i  The  pupil  should  acquire  immediate  familiarity  with  these  expressions,  which 
occur  so  frequently  in  Physics,  and  in  this  connection  should  practice  writing 
inverse  proportions.  Thus,  for  the  quantities  here  given,  14  :  6  =  $  :  *,  i.e.  the  forces 
are  proportional  to  the  reciprocals  of  their  respective  distances  from  the  resultant. 


46  MOLAR    DYNAMICS. 

the  extremity  of  the  axis  about  which  A  B  is  supposed  to  rotate. 
The  perpendicular  distance  (C  A  or  C  B)  from  the  axis  of  rota- 
tion to  the  line  of  direction  in  which  a  force  acts  (A  D  or  B  E) 
is  called  the  leverage  of  the  force. 

The  moment  of  a  force  is  measured  by  the  product  of  the 

intensity  of  the  force  into  its  lever- 
age. For  example,  the  moment 
of  the  force  A  D  (Fig.  25)  is  ex- 
pressed numerically  by  the  num- 
ber (30  x  2  =)  60,  and  the  moment 
pm  26  of  B  E  is  (20  X  3  =)  60.  By  defini- 

tion the  line  A  C  (Fig.  26)  is  the 
leverage  of  force  a  P,  and  B  C  of  the  force  b  Q. 

48.  Equilibrium  of  Moments.  The  moment  of  a  force  is 
said  to  be  positive  when  it  tends  to  produce  right-hand  rotation, 
i.e.  rotation  in  the  direction  in  which  the  hands  of  a  clock  move, 
and  negative  when  its  tendency  is  in  the  reverse  direction. 
If  two  forces  act  at  different  points  of  a  body  which  is  free  to 
rotate  about  a  fixed  point,  they  will  produce  equilibrium  when 
the  algebraic  sum  of  their  moments  is  zero.  Thus,  the  moment 
of  the  force  applied  at  A  (Fig.  25)  is  -  (30  X  2)  =  -  60.  The 
moment  of  the  force  applied  at  B  in  an  opposite  direction  is 
accordingly  +  (20  X  3)  =  +  60.  Their  algebraic  sum  is  zero, 
and  consequently  there  is  equilibrium  between  the  moments, 
and  no  tendency  to  rotation. 

When  more  than  two  forces  act  in  this  manner  there  will 
be  equilibrium  if  the  3 

algebraic   sum    of   all          0| 

the  moments  (positive    201     J5       — ? — ^—  — •£. .30 

and  negative)  be  zero.     c  d\  e\  f\ 

Thus,  the  equation  of     ^  J  ^  J^ 

moments  acting  about  FIG.  27. 

the  axis  D  (Fig.  27)  is  ([/]  45  +  [e]  25  +  [a]  30)  +  ([e]  -  30 


MOMENT    OF    A    COUPLE.  47 

[ef]  —  40  [&]  —  30)  =  0 ;   the  sum  of  all  the  moments  being 
zero,  there  is  equilibrium  of  moments. 

49.  Moment  of  a  Couple.     The  moment  of  a  couple,  or  its 
value  in  producing  rotation,  is  the  sum  of  Fi 

the  moments  of  its  two  components  about 
the  axis  of  rotation.     Let  F  and  FI  (Fig.  28) 

constitute  a  couple  whose  points  of  applica-      P L 

tion  are    A  and  B.      To   find  the   rotating 

value  of   the  couple,  let  P  be  the  axis  of 

rotation ;    then   the    moments    of    F  and   FI 

relatively  to    P  are    F  X  A  P,  and   FI  X  B  P.  FlG  28- 

The  total  resultant  moment  of  the  two  forces  is  (F  X  A  P)  4- 

(Fi  X  B  P),  or  (since  F  =  FI)   F  X  A  B. 


EXERCISES. 

1.  Two  parallel  forces  of  8  Ibs.  and  12  Ibs.  act  in  the  same  direction, 
respectively  at  points  A  and  5,  12  inches  apart.     Find  the  magnitude 
and  position  of  their  resultant. 

2.  The  smaller  of  two  parallel  forces  having  the  same  direction  is  5 
inches  from  the  resultant.     What  is  the  distance  of  the  resultant  from 
the  other  force  ? 

3.  Two  men  carry  a  weight  of  100  Ibs.  suspended  from  a  pole  15  feet 
long ;  each  man  is  18  inches  from  his  end  of  the  pole.     Where  must  the 
weight  be  attached  in  order  that  one  man  may  bear  f  of  it  ? 

4.  Take  from  the  last  problem  the  number  of  pounds  supported  by 
each  man  and  the  respective  distances  of  each  from  the  weight,  and 
make  an  inverse  proportion  which  shows  the  relation  that  must  exist 
between  these  quantities. 

5.  How  can  a  force  of  4  Ibs.  be  made  to  produce  equilibrium  with  a 
force  of  12  Ibs.  ? 

6.  Draw  a  line  2  inches  long.     Represent  on  a  scale  of  \  inch  =  1  Ib. 
a  force  of  8  Ibs.  applied  at  a  point  A,  \  of  1  inch  from  one  end  of  the  line 
and  at  right  angles  to  it.    Take  for  the  axis  of  rotation  a  point  B,  f  inch 
from  the  same  end  of  the  line.    From  point  0,  \  inch  from  the  other  end 


48  MOLAR*  DYNAMICS. 

of  the  line  draw  a  line  which  will  represent  a  force  that  will  produce 
equilibrium  with  the  first  force,  and  thereby  prevent  rotation. 

7.  Repeat  the  work  of  the  last  problem,  but  assume  that  the  force 
applied  at  A  acts  obliquely  on  the  line. 

8.  Can  a  single  force  produce  equilibrium  with  a  couple  ? 

9.  (a)  A  plank  weighing  40  Ibs.  is  placed  across  a  log  so  as  to  be 
balanced.     A  boy  weighing  60  Ibs.  sits  on  one  end  of  the  plank.     Where 
shall  another  boy  weighing  90  Ibs.  sit  that  he  may,  balance  the  first  ? 
(6)  What  pressure  will  be  exerted  upon  the  log  ? 

10.  Two  horses  harnessed  abreast   are   ploughing.      How  can  you 
arrange  that  one  horse  shall  pull  only  two  thirds  as  much  as  the  other  ? 

11.  The  maximum  muscular  force  which  a  certain  man  can  exert  is 
200  Ibs.     With  what  leverages  can  he  raise  a  stone  weighing  a  ton  ? 

12.  How  can  pressure  be  multiplied  indefinitely  ? 

13.  Three  forces  of  2,  10,  and  12  units  act  on  a  body  along  parallel 
lines.     Show  how  they  may  be  adjusted  so  as  to  be  in  equilibrium  ? 

14.  A  force  of   10  units  has  a  moment  about  a  certain  axis  of  75 
units.     How  many  units  of  distance  is  the  axis  from  the  line  of  action  of 
the  force  ? 


SECTION   VI. 

CFNTER  OF  MASS  OR  CENTER  OF  INERTIA. 

50.  Center  of  Mass  Defined.  Let  Fig.  29  represent  any 
body  of  matter,  e.g.  a  stone.  Every  particle  of  the  body  is 
acted  upon  by  the  force  of  gravitation. 
The  gravitation  forces  acting  on  the 
particles  form  a  set  of  parallel  forces, 
the  resultant  of  which  equals  their  sum 
(§  45),  and  has  the  same  downward 
direction  as  its  components.  In  what- 
ever position  the  body  may  be,  the  result- 
ant passes  through  a  definite  point  in  it  ; 
this  point  is  called  the  center  of  mass 
or  center  of  inertia  of  the  body.  The 
center  of  mass  (c.m.)  of  a  body  is,  therefore,  the  point  of  appli- 


CENTER    OF    MASS    DEFINED.  49 

cation,  of  the  resultant  of  all  the  gravitation  forces  ;  and  for 
many  practical  purposes  the  whole  mass,  weight,  or  inertia  of 
the  body  may  be  supposed  to  be  concentrated  at  this  point.1 

Let  G  (Fig.  29)  represent  the  c.m.  of  the  stone.  For 
practical  purposes,  then,  we  may  consider  that  the  force  of 
gravitation  acts  only  at  this  point,  and  in  the  direction  G  F. 
If  the  stone  fall  freely,  this  point  cannot  deviate  from  a 
vertical  path,  however  much  other  points  of  the  body  may 
rotate  about  this  point  during  its  fall.  Inasmuch,  then,  as 
the  c.m.  of  a  falling  body  always- describes  a  definite  path,  a 
line,  G  F,  that  represents  this  path,  or  the  path  in  which  a 
body  supported  tends  to  move,  is  called  the  line  of  direction. 
It  may  be  defined  as  the  straight  line  in  which  lie  the  center 
of  mass  of  the  body  and  the  center  of  mass  of  the  earth  ;  its 
direction  is  always  vertical. 

To  support  any  body,  then,  it  is  only  necessary  to  provide 
a  support  for  its  center  of  mass.  The  supporting  force  must  be 
applied  somewhere  in  the  line  of  direction.  The  difficulty  of 
poising  a  book,  or  any  other  object,  on  the  end  of  a  finger 
consists  in  keeping  the  support  under  its  center  of  mass,  i.e. 
in  the  line  of  direction. 


! '  PHB»H^W8Pffv!!W^^^^W 


Fig.  30  represents  a  toy  called  a  "witch,"  consisting  of  a  cylinder  of 
pith  terminating  in  a  hemisphere  of  lead.    The 
toy  will  not  lie  in  a  horizontal  position,  as 
shown  in  the  figure,  because  the  support  is  Gl 
not  applied  immediately  under  its  c.m.  at  G  ; 
but  when  placed  horizontally  it  immediately 
assumes  a  vertical  position.     It  appears  to  the 

observer  to  rise  ;  but,  regarded  in  a  technical  sense,  it  really  falls,  because 
its  c.m.  takes  a  lower  position. 

1  The  expression  center  of  mass  does  not  necessarily  signify  that  point  occupying 
a  central  position  among  the  particles  of  a  body,  but  a  point  where,  for  convenience 
in  some  dynamical  problems,  we  may  consider  all  the  mass  (or  inertia)  to  be  concen- 
trated. The  center  of  mass  is  often  called  the  center  of  gravity.  By  the  place  or 
the  Inc'ition  of  a  body  mathematicians  mean  the  point  where  its  center  of  mass  is 
situated.  Thus,  in  dynamical  problems  the  distances  between  celestial  bodies,  as 
the  sun,  moon,  and  earth,  are  the  distances  between  their  centers  of  mass. 


50 


MOLATl    DYNAMICS. 


51.  How  to  Find  the  Center  of  Mass  of  a  Body,    imagine  a 

string  to  be  attached  to  a  potato,  as  in  Fig.  31,  and  to  be  suspended  from 
the  hand.  When  the  potato  is  at  rest,  there  is 
an  equilibrium  of  forces,  and  the  c.m.  must  be 
somewhere  in  the  line  of  direction  o  n.  Sus- 
pend the  potato  from  some  other  point,  as  b, 
and  the  c.m.  must  be  somewhere  in  the  new 
line  of  direction,  b  s.  Since  the  c.m.  lies  in 
both  the  lines  a  n  and  b  s,  it  must  be  at  c,  their 
point  of  intersection.  It  will  be  found  that, 
from  whatever  point  the  potato  is  supported, 
the  point  c  will  always  be  vertically  under  the 
point  of  support.  In  a  similar  manner  the  c.m. 
of  any  body  may  be  found.  But  the  c.m.  of  a 
body  may  not  be  coincident  with  any  particle  of  the  body ;  for  example, 
the  c.m.  of  a  ring,  a  hollow  sphere,  etc. 

The  center  of  mass  of  any  symmetrical  body  of  uniform  density  coin- 
cides with  its  geometrical  center.  Examples  :  the  middle  point  of  a  mate- 
rial straight  line ;  that  point  on  a  straight  line  joining  the  vertex  to  the 
middle  of  the  base  of  a  triangle  which  is  situated  at  a  distance  from  the 
vertex  equal  to  two  thirds  the  length  of  the  line  ;  the  geometrical  center 
of  any  polygon,  of  a  sphere,  of  a  circular  cylinder. 

52.  Equilibrium  of  Bodies.     A  body  will  rest  in  equilib- 
rium when  its  line  of  direction  passes  through  its  point  of 
support.     A  body  will  be'supported  at  its  base  when  its  line 
of  direction  falls  within  its  base  or  lowest  side.     [The  base 
of  any  body,  e.g.  a  chair,  is  the  polygon  formed  by  joining  by 
straight  lines  the  points  of  support.]     There  are  three  kinds 
of  equilibrium  : 

(1)  A  body  so  supported  that  when  slightly  disturbed  it  tends  to  return 
to  its  original  position  is  said  to  be  in  stable  equilibrium.     This  will  be 
the  case  whenever  such  a  disturbance  raises  its  c.m.  ;  for  the  weight  of 
the  body  acting  at  its  c.m.  tends  to  bring  this  point  as  low  as  possible,  and 
thus  causes  it  to  return  to  its  former  position.     Evidently  a  body  is  in 
stable  equilibrium  when  the  supporting  force  is  applied  in  the  line  of 
direction  above  its  c.m. 

(2)  A  body  so  supported  that  a  slight  disturbance  tends  to  cause  it  to 
take  a  new  position  with  its  c.m.  lower  than  before  .is  in  unstable  equi- 
librium. 


STABILITY    OF    BODIES. 


51 


(3)  A  supported  body  whose  c.m.  is  neither  raised  nor  lowered  by  a 
disturbance  is  in  neutral  equilibrium. 

For  example,  a  cylinder,  if  it  be  uniformly  dense,  is  in  neutral  equi- 
librium when  placed  on  its  side  upon  a  horizontal  plane,  and  it  rests 
equally  well  in  all  positions.  But  if,  on  account  of  unequal  density,  its 
c.m.  be  not  in  its  axis,  then  its  equilibrium  is  stable  when  its  c.m.  is 
below  its  axis,  and  unstable  when  it  is  above  it. 

53,  Stability  of  Bodies.  The  ease  or  difficulty  with  which 
bodies  supported  at  their  bases  are  overturned  varies  with  the 
hight  to  which  their  c.m.  must  be  raised  to  overturn  them. 
The  letter  c  (Fig.  32)  marks  the  position  of  the  c.m.  of  each  of 
the  four  bodies  A,  B,  C,  and  D.  If  any  one  of  these  bodies  be 
overturned,  its  c.m.  must  pass  through  the  arc  c  i,  and  be 
raised  through  the  hight  a  i.  By  comparing  A  with  B,  and 
supposing  them  to  be  of  equal  weight,  we  learn  that  in  over- 
turning two  bodies  of  equal  iveight  and  hight  of  c.m.,  the  c.m. 
of  that  body  which  has  the  larger  base  must  be  raised  higher, 


i 

a 

a 
] 

M= 

i 
a 

-^ 

c-= 

j 

A 

B 

C 

?IG.  32. 

D 

and  that  body  is,  therefore,  overturned  with  greater  difficulty. 
A  comparison  of  A  and  C,  supposing  them  to  be  of  equal 
weight,  shows  that  ivhen  two  bodies  have  equal  bases  and 
weights,  the  body  having  its  c.m.  higher  is  more  easily  over- 
turned. D  and  C  have  equal  masses,  bases,  and  hights,  but 
D  is  made  heavy  at  the  bottom,  and  this  lowers  its  c.m.  and 
gives  it  greater  stability. 


52 


MOLAR    DYNAMICS. 


EXERCISES. 

1.  Where  is  the  c.m.  of  a  box  ? 

2.  Why  is  a  pyramid  a  very  stable  structure  ? 

3.  What  is  the  object  of  ballast  in  a  vessel  ? 

4.  State  several  ways  of  giving 
stability  to  an  inkstand. 

5.  (a)    In   what   position    would 
you  ^place  a  cone   on  a   horizontal 
plane  that  it  may  be  in  stable  equi- 
librium ?      (b)    That  it  may  be  in 
neutral  equilibrium?      (c)    That  it 
may  be  in  unstable  equilibrium  ? 

6.  In    loading    a   wagon,    where 
should  the  heavy  luggage  be  placed  ? 
Why  ? 

7.  Why    are    bipeds    slower    in 
FIG.  33.                          learning  to  walk  than  quadrupeds  ? 

8.  Why  is  mercury  placed  in  the  bulb  of  a  hydrometer  ? 

9.  How  will  a  man  by  rising  in  a  boat  affect  its  stability? 

10.  Which  is  more  liable  to  be  overturned,  a  load  of 
hay  or  a  load  of  stone  of  equal  weight  ? 

11.  What  attitude  does  a  man  assume  when  carrying 
a  heavy  load  on  his  back  ?    Why  ? 

12.  What  position  do  bodies  floating  in  air  or  in  water 
take? 

13.  (a)  Explain   how  the  toy  horse    (Fig.  33)  stands 

upon  the  platform  without  falling  off.  (b) 
Explain  how  the  toy  may  rock  upon  its 
support  without  falling  off. 

14.  It  is   difficult  to  balance   a  lead 
pencil  on  the  end  of  a  finger ;    but  by 
attaching  two  knives  to  it,  as  in  Fig.  34, 
it  may  be  rocked   to  and  fro  without 
falling.     Explain. 

15.  If  the  end  C  of  the  triangular  frame 
A  B  (Fig.  35)  be  raised  and  allowed  to  fall, 

the  frame  will  rock  to  and  fro  on  its  support,  and  finally  come  to  rest  in  its 
original  position,  (a)  What  kind  of  equilibrium  has  it  ?  (b)  If  the  weight 
at  the  end  B  be  removed, will  the  frame  be  supported  by  the  table?  (c)  Why? 


FIG.  34. 


FIG.  35. 


PARALLELOGRAM    OF    FORCES. 


53 


SECTION   VII. 


FIG.  36. 


COMPOSITION    OF    FORCES    ACTING   AT    ANGLES  WITH 
ONE    ANOTHER. 

54,  Parallelogram  of  Forces.  If  two  forces  having  a 
common  point  of  application  act  at  an  angle  with  each  other, 
their  resultant  and  equilibrant  may  be  ascertained  by  means 
of  the  "parallelogram  of  forces, "as  the 
following  experiment  will  illustrate  : 

Experiment.  Insert  pegs  in  any  three 
holes  of  the  circle  in  the  top  of  the  circular 
table,  Fig  36.  Join  these  by  threads  attached 
to  spring  balances  as  shown  in  the  figure. 
Stretch  the  balances  so  as  to  indicate  any  de- 
sired pull  in  each  of  the  threads.  Place  under 
the  threads  a  sheet  of  white  paper.  Locate 
on  the  paper  the  common  point  of  application 
A  of  the  three  forces.  Draw  lines  A  B,  AC, 
and  A  D  to  represent  the  directions  in  which 
the  forces  act.  Since  the  point  A  does  not  move,  it  is  evident  that  the 
three  forces  are  in  equilibrium,  and  that  any  one  of  the  three  forces  is  the 
equilibrant  of  the  other  two.  Select  any  one  for  an  equilibrant  (e.g.  A  D) 
and  extend  it  in  an  opposite  direction  from  A,  representing  (on  some 
suitable  scale)  a  force  A  E  equal  to  and  opposite  to  the  force  A  D  as  indi- 
cated by  the  dynamometer  D.  On  the  same  scale  lay  off  distances  A  B 
and  A  C  representing  the  magnitudes  of  the  forces  acting  in  the  direc- 
tions of  these  lines.  The  line  A  E  is  by  definition  the  resultant  of  A  B 
and  A  C.  Connect  E  with  C  and  B.  The  figure,  if  the  work  be  done 
with  care,  will  be  found  to  be  a  parallelogram.  The  diagonal  E  A  repre- 
sents the  magnitude  of  the  resultant  of  the  forces  A  B  and  A  C,  and  the 
same  line  with  the  direction  reversed  (i.  e.  A  E)  represents  the  equilibrant. 

If  two  forces  applied  at  a  point  be  represented  in  magnitude 
and  direction  by  the  adjacent  sides  of  a  parallelogram  drawn 
from  the  common  point  of  application,  their  resultant  will  be 
represented  in  magnitude  and  direction  by  the  diagonal  which 
passes  through  that  point. 


54 


MOLAR   DYNAMICS. 


This  proposition  is  applicable  whether  the  forces  act  on  a  particle  or 
on  a  rigid  body  of  any  size  provided  they  lie  in  the  same  plane.     Thus, 


FIG.  37. 

let  two  forces  applied  at  points  A  and  B  of  a  stone  (Fig.  37)  act  in  the 
directions  A  C  and  B  D,  respectively.  The  direction  of  the  resultant 
must  pass  through  E,  the  point  where  the  lines  of  direction  of  the  given 
forces  when  produced  backwards  intersect.  If,  now,  the  lines  E  C  and 
E  D  be  laid  off  to  represent  the  relative  intensities  of  the  forces,  the 
diagonal  E  F  of  the  parallelogram  constructed  thereon  will  represent 
their  resultant,  and  its  point  of  application  may  be  G  or  any  other  point 
in  the  line  G  H. 

55.  Composition  of  More  than  Two  Forces  in  the  Same 
\B  Plane.  When  more  than  two  com- 
ponents are  given,  find  the  resultant 
of  any  two  of  them,  then  that  of 
this  resultant  and  a  third,  and  so  on 
till  every  component  has  been  used. 
Thus,  in  Fig.  38,  A  C  is  the  result- 
ant of  A  B  and  A  D,  and  A  F  is  the 
resultant  of  A  C  and  A  E,  i.e.  of 


FIG.  38. 


the  three  forces  A  B,  AD,  and  A  E. 


RESOLUTION   OF   FORCES. 


55 


Generally  speaking,  a  motion  may  be  the  result  of  any 
number  of  forces.  When  we  see  a  body  in  motion,  we  can- 
not determine  by  its  behavior  how  many  forces  have  con- 
curred to  produce  its  motion. 

56.  Resolution  of  Forces,  Assume  that  a  ball  has  an 
acceleration  in  a  certain  direction  A  C  (Fig.  39),  and  that  one 
of  the  forces  that  produces  this  acceleration  is  represented  in 
intensity  and  direction  by  the  line  A  B ;  what  must  be  the 
intensity  and  direction  of  the  other  force  ?  Since  A  C  is  the 
resultant  of  two  forces  acting 
at  an  angle  to  each  other,  it 
is  the  diagonal  of  a  parallelo- 
gram of  which  A  B  is  one  of 

the  sides.    From  C,  draw  C  D    ^i^^ t /D 

parallel  and  equal  to  B  A,  and  FIG.  39. 

complete   the   parallelogram 

by  connecting  the  points  B  and  C,  and  A  and  D.  Then,  according 
to  the  principle  of  composition  of  forces,  A  D  represents  the 
intensity  and  direction  of  the  force  which,  combined  with 
the  force  A  B,  would  give  the  ball  an  acceleration  A  C.  The 
component  A  B  being  given,  no  other  single  force  than  A  D  will 
satisfy  the  question.  Had  the  question  been,  "  What  forces 
can  produce  the  motion  AC?"  an  infinite  number  of  answers 
might  have  been  given. 

It  is  often  necessary  to  resolve  a  force  in  order  to  ascertain  the  effect- 
ive force  in  a  certain  direction.  Thus,  when  boat  sails  are  exposed 

obliquely  to  the  wind, 
the  pressure  effectual  in 
moving  the  boat  is  only 
a  component  of  the 
whole  force  of  the 
wind.  The  line  a  f  (Fig. 
40)  represents  the  force 
of  the  wind  acting  on 
the  sail  c  d  at  the 
FIG.  40.  point  a.  Resolving  this 


,f 


56 


MOLAR    DYNAMICS. 


force  we  obtain  the  components  2  (normal  to  the  sail)  and  I  (a  useless 
component  called  a  tail  wind).  The  boat  does  not  move  in  the  direction 
of  the  pressure  on  its  sail,  because  it  is  more  easily  moved  lengthwise 
than  breadthwise.  Hence  the  normal  pressure  must  be  resolved  into  two 
components,  one  4  along  the  direction  of  least  resistance,  i.e.  the  direc- 
tion of  easy  motion,  the  other  3  at  right  angles  to  it.  The  component 
4  drives  the  boat  forward.  The  component  3  tends  to  cause  a  slow 
broadside  motion  called  leeway,  but  this  may  be  partly  counteracted  by 
a  deep  keel  or  a  center-board,  so  that  the  boat  will  sail  approximately 
along  the  line  a  b. 

EXERCISES. 

1.  What  is  the  greatest  and  what  the  least  resultant  of  two  forces  of 
151bs.  and  17  Ibs.? 

2.  Draw  upon  paper  pairs  of  lines  making  about  the  same  angles 
with  each  other  as  A  B  and  A  C  in  the  four  diagrams,  Fig.  41,  and  having 


B    B 


FIG.  41. 

about  the  same  directions  ;  assign  numerical  values  arbitrarily  to  each 
component,  drawing  to  scale,  and  find  the  direction  and  the  numerical 
value  of  the  resultant  of  each  pair  of  components. 

3.  Two  forces  of  20  Ibs.  and  30  Ibs.  act  at  an  angle  of  90°.     Find  the 
intensity  of  their  resultant  without  constructing  a  parallelogram. 

4.  Resolve  a  force  of  40  Ibs.  into  two  components  at  right  angles  to 
each  other,  one  of  the  forces  to  be  15  Ibs. 

5.  A  weight  of  50  k.  is  supported  by  two  strings  inclined  to  the  verti- 
cal at  30°  and  60°.     Find  the  tension  of  each  string. 

6.  What  three  conditions  are  requisite  that  a  force  may  be  in  equi- 
librium with  two  parallel  forces  ? 

7.  Draw  a  line  to  represent  a  force  of  20  Ibs.  acting  at  an  angle  of  30° 
with  a  horizontal  line,  and  find  its  efficiency  in  a  vertical  direction. 

8.  The  resultant  of  two  equal  forces  acting  upon  a  point  at  an  angle 
of  90°  is  10  Ibs.    Find  the  value  of  each  component. 


HOW    CURVILINEAR    MOTION    IS    PRODUCED. 


57 


SECTION   VIII. 


CURVILINEAR   MOTION. 

57.  How  Curvilinear  Motion  is  Produced.  Motion  is  curvi- 
linear when  its  direction  changes  at  every  point.  But 
according  to  the  First  Law  of  Motion,  every  moving  body 
proceeds  in  a  straight  line  unless  compelled  to  depart  from  it 
by  some  external  force.  Hence,  curvilinear  motion  can  be 
produced  only  by  an  external  force  acting  continuously  upon 
the  body  at  an  angle  to  the  straight  path  in  which  the  body 
tends  to  move,  so  as  constantly  to  change  its  direction.  In 
case  the  body  moves  in  a  circle,  this  force  acts  at  right  angles 
to  the  path  of  the  body  or  towards  the  center  of  motion  ;  hence, 
this  deflecting  force  has  received  the  name  of  central  force. 

Thus,  suppose  a  ball  at  A  (Fig.  42),  suspended  by  a  string  from  a  point 
d,  to  be  struck  by  a  bat  in  such  a  manner  that  it  tends  to  move  in  the 
direction  A  o.  As  it  is  restrained  from  taking  that  path  by  the  tension 
of  the  string,  which  operates  like  a  force- 
drawing  it  toward  d,  it  takes,  in  obedience 
to  the  two  forces,  an  intermediate  course. 
At  c  its  motion  is  in  the  direction  c  n,  in 
which  path  it  would  move  but  for  the  string, 
in  accordance  with  the  First  Law  of  Motion. 
Here,  again,  it  is  compelled  to  take  an  inter- 
mediate path.  Thus,  at  every  point  the 
tendency  of  the  moving  body  is  to  preserve 
the  direction  it  has  at  that  point  and  con- 
sequently to  move  in  a  straight  line.  The 
only  reason  it  does  not  so  move  is  that  it  is 
at  every  point  forced  from  its  natural  path  by  the  pull  of  the  string. 
But  if  the  string  be  cut  when  the  ball  reaches  the  point  i,  the  ball,  having 
no  force  operating  to  change  its  motion,  continues  in  the  direction  in 
which  it  is  moving  at  that  point,  i.e.  in  the  direction  i  h,  which  is  tangent 
to  its  former  circular  path. 

If  the  free  end  of  the  string  be  held  in  the  hand,  the  ball  while  revolv- 
ing about  the  hand  appears  to  pull  the  hand.  But  it  is  evident  that  no 
force  acts  upon  the  ball  except  the  pulling  force  exerted  by  the  hand 


58  MOLAR   DYNAMICS. 

through  the  string,  and  that  this  apparent  pull  on  the  part  of  the  ball  is 
only  the  effect  of  the  reaction  of  the  force  exerted  by  the  hand  upon  the 
ball.  This  reaction  is  erroneously  called  *'  centrifugal  force." 

There  is  no  centrifugal  force  ;  there  is  no  "tendency  to  fly  off  from 
the  center"  ;  arid  there  is  no  tendency  of  any  kind  that  is  not  fully 
explained  by  the  First  Law  of  Motion. 

58,  Law  of  Central  Force.     For  a  body  moving  in  a  circular 
orbit  the  central  force  is  proportional  to  the  mass  of  the  body 
and  to  the  square  of  its  velocity,  and  inversely  proportional  to 
its  distance  from  the  center  of  motion. 

Let  f  represent  the  central  force,  m  the  mass  of  the 
revolving  body,  v  its  velocity,  and  r  the  radius  of  the  circle, 
and  the  law  may  be  expressed  in  the  following  formula  : 

mv* 
*-''" 

The  farther  a  point  is  from  the  axis  of  motion,  the  farther 
it  has  to  move  during  a  rotation ;  consequently  the  greater 
must  be  its  velocity  to  complete  a  revolution  in  a  given  time. 
Hence,  of  bodies  upon  the  earth's  surface,  those  situated  at  the 
equator  have  the  greatest  velocity  due  to  the  earth's  rotation, 
and  consequently  the  greatest  tendency  to  fly  off  from  its  sur- 
face. The  effect  of  this  is  to  neutralize,  in  some  measure,  the 
force  of  gravity.  It  is  calculated  that  a  body  weighs  about 
si?  less  at  the  equator  than  at  either  pole,  in  consequence  of 
the, greater  tangential  tendency  at  the  former  place.  But  289 
is  the  square  of  17 ;  hence,  if  the  earth's  velocity  were  in- 
creased seventeenfold,  objects  at  the  equator  would  weigh 
nothing,  i.e.  the  tangential  tendency  would  be  equal  to  their 
weight. 

59.  Tendency  to  Rotate  Around  the  Shortest  Axis.     It  can 
be  demonstrated  mathematically,  as  well  as  experimentally, 
that  a  freely  rotating  body  is  in  stable  equilibrium  only  when 
rotating  about  its  shortest  diameter ;   hence  the  tendency  of 
a  rotating  body  to  take  this  position. 


ROTATION   ABOUND   THE   SHORTEST   AXIS. 


59 


FIG.  43. 

Experiment.    Arrange  some  kind  of  rotating  apparatus,  e.g.  R  (Fig. 
43).     Suspend  a  skein  of  thread,  a  (Fig.  44),  by  a  string,  and  cause  it  to 
rotate ;  it  assumes  the  shape  of  the 
oblate  spheroid  a'.      A  chain,  b,  as- 
sumes a  similar  form.     Pass  a  string 
through  the  longest  diameter  of  an 
onion,  c,  and  cause  it  to  rotate  ;  the 
onion  gradually  changes  its  position 
so  as  to  rotate  on  its  shortest  axis. 

Mount  a  glass  globe,  G  (Fig.  43), 
about  one  tenth  full  of  colored  water, 
and  cause  it  to  rotate.  The  liquid 
gradually  leaves  the  bottom,  rises, 

and  forms  an  equatorial  ring  within  the  glass.    In  a  similar  way  the  water 
of  the  earth's  great  ocean  is  "  heaped  up  "  at  the  earth's  equator. 


FIG.  44. 


EXERCISES. 

1.  (a)  What  is  the  cause  of  the  stretching  force  exerted  on  the  rubber 
cord  when  you  swing  a  return  ball  about  your  hand  ?     (6)  Suppose  that 
you  double  the  velocity  of  the  ball,  how  many  times  shall  you  increase 
this  stretching  force  ? 

2.  Why  do  wheels  and  grindstones,  when  rapidly  rotating,  tend  to 
break,  and  the  pieces  to  fly  off  ? 


60  MOLAR   DYNAMICS. 

3.  On  what  does  the  magnitude  of  the  pull  between  a  rotating  body 
and  its  center  of  motion  depend  ? 

4.  (a)  Explain  the  danger  that  a  carriage  will  be  overturned  in  turn- 
ing a  corner.     (6)  How  many  fold  is  the  tendency  to  overturn  increased 
by  doubling  the  velocity  of  the  carriage  ? 

5.  Account  for  the  curvilinear  orbits  of  the  planets. 

6.  How  are  their  motions  in  their  orbits  and  around  their  axes  main- 
tained ? 

7.  In  what  way  should  the  rails  be  laid  in  order  to  neutralize  the 
tangential  tendency  of  a  railroad  train  when  going  around  a  curve  ? 

8.  State  and  explain  the  posture  of  a  bicycle  rider  in  turning  a  curve. 

9.  In  what  way  is  the  weight  of  terrestrial  bodies  nullified  in  some 
degree  by  the  earth's  motion  ? 

10.  A  circus  rider  going  around  a  ring  inclines  inward  so  that  the  line 
of  direction  of  his  body  falls  without  his  base.     How  is  he  supported  ? 

SECTION   IX. 

THE   PENDULUM. 

60.  Dynamics  of  the  Pendulum.     When  a  pendulum  bob, 
B  (Fig.  45),  is  raised,  the  force  of  gravity  acting  on  it,  repre- 
sented by  the  line  B  G,  may  be  resolved  into  two  components, 
s  one  of  which,  B  C,  acts  upon  the  point  of  sup- 

port S,  while  the  other,  B  D,  acts  at  right 
angles  to  it,  producing  acceleration  toward  0. 
Its  inertia  carries  it  beyond  0  against  the 
action  of  gravity,  which  gives  it  a  negative 
acceleration  and  brings  it  to  rest  at  M.  The 
backward  swing  from  M  to  B  is  explained  in 
the  same  way.  Thus  the  pendulum  oscillates 
under  the  action  of  gravity,  which  reverses 
its  acceleration  at  point  0  during  each  swing. 
The  motion  from  one  extremity  of  the  arc 
through  which  a  pendulum  swings  to  the  other  is  called  a 
vibration  or  an  oscillation.  The  time  occupied  by  the  pendulum 
in  moving  once  over  this  arc  is  called  the  time  or  period  of  vi- 
bration, and  the  angle  B  S  0  is  called  the  amplitude  of  vibration. 


LAWS    OF    THE    PENDULUM. 


61 


61.  Laws  of  the  Pendulum, 

Experiment  1.  From  a  bracket  suspend  by  strings  leaden  balls,  as  in 
Fig.  46.  Draw  B  and  C  to  one  side,  and  to  different  bights,  so  that  B 
may  swing  through  a  short  arc  and  C  through  a  longer  arc,  and  let  both 
drop  at  the  same  instant.  C  moves  faster  than  B,  and  completes  a  longer 
journey  at  each  swing,  but  both  complete  their  swing,  or  vibration,  in 
the  same  time. 

Hence,  (1)  the  time  occupied  by  the  vibration  of  a  pendulum 
is  independent  of  the  length  of  the  arc. 

Of  only  very  small  arcs  may  this  law  be  regarded  as  practically  true. 
The  pendulum  requires  a  somewhat  longer  time  for  a  long  arc  of  vibra- 
tion than  for  a  short  one,  but  the  differ- 
ence becomes  perceptible  only  when  the 
difference  between  the  arcs  is  great,  and 
then  only  after  many  vibrations. 


Experiment  2.  Set  all  the  balls 
swinging ;  only  B  and  C  swing  together ; 
the  shorter  the  pendulum,  the  faster  it 
swings.  Make  B  1  m.  long  and  F  J  m.  long. 
With  watch  in  hand,  count  the  vibrations 
made  by  B.  It  completes  60  vibrations 
in  a  minute  ;  in  other  words,  it  "beats 
seconds."  A  pendulum,  therefore,  to 
beat  seconds  must  be  1  m.  long  (more  ac- 
curately in  the  latitude  of  Boston  at  sea 
level  .9935  m.,  or  39.117  in.).  Count  the 
vibrations  of  F  ;  it  makes  120  vibrations 
in  the  same  time  that  B  makes  60  vibra- 
tions. Make  G  one  ninth  the  length  of  B  ; 
the  former  makes  three  vibrations  while 
the  latter  makes  one,  consequently  the  time  of  vibration  of  the  former  is 
one  third  that  of  the  latter. 

Hence,  (2)  the  time  of  one  vibration  of  a  pendulum  varies  as 
the  square  root  of  its  length. 

The  length  I  of  a  simple  pendulum  which  shall  swing  in  a 
time  t,  or  the  time  of  swing  for  a  length  I,  can  be  found  from 
the  formulae : 


B   C 
FIG.  46. 


62  MOLAR   DYNAMICS. 


I  =  .9935  X  t2,  whence  t  =  \      l     for  I  meters  : 

\  QQQFC 


.9935 

inches. 


or        I  =  39.117  X  t*,  whence  t  =  \ for  I  i 

X39.117 

By  experiments  too  difficult  for  ordinary  school  work,  it 
has  been  ascertained  that  (3)  the  time  of  vibration  of  a  pendu- 
lum varies  inversely  as  the  square  root  of  the  force  of  gravi- 
tation (upon  which  the  value  of  g  depends). 

To  sum  up  the  above  three  laws  of  the  pendulum,  we  have 
the  formula  : 1 


t  —  TT  A/_,  whence  g  =  — , 

^<7  *2 

in  which  Z  =  length  of  pendulum  ;  t  =  time  of  one  vibration 
in  seconds. 

62.  Simple  Pendulum  ;  Center  of  Oscillation.  A  simple 
pendulum  is  a  material  particle  supported  by  a  weightless 
thread.  Such  a  pendulum  can  exist  only  in  the  imagination, 
but  the  conception  is  useful.  Every  real  pendulum  is  a  com- 
pound pendulum,  which  may  be  supposed  to  be  composed  of  as 
many  simple  pendulums  bound  together  as  there  are  particles 
in  the  pendulum.  Those  particles  nearest  the  point  of  suspen- 
sion tend  to  quicken,  and  those  farthest  away  tend  to  check, 
the  motion  of  the  combination.  It  is  apparent  that  there 
must  be  in  every  compound  pendulum  a  particle  so  situated 
that  its  motion  is  neither  quickened  nor  checked  by  the  com- 
bined action  of  the  particles  above  and  below  it.  The  loca- 
tion of  this  particle  is  called  the  center  of  oscillation.  The 
real  length  of  a  compound  pendulum  is  the  distance  of  this 
point  from  the  point  of  suspension,  and  it  is  this  length  that 
is  referred  to  in  the  laws  of  the  pendulum. 

1  The  student  may  find  the  development  of  this  formula  in  Chapter  VII  of 
Maxwell's  "  Matter  and  Motion." 


USES    OP    THE    PENDULUM.  63 

The  center  of  oscillation  of  a  pendulum,  may  be  found 
approximately  as  follows  :  A.  small  lead  ball  suspended  by  a 
thread  is  a  near  approximation  to  a  simple  pendulum,  and 
the  distance  from  the  center  of  the  ball  to  the  point  of  sus- 
pension may  be  taken  as  the  length  of  this  pendulum. 
Suspend  from  the  same  support  this  pendulum  and  the  pendu- 
lum whose  center  of  oscillation  is  to  be  found.  For 

A 

example,  let  the  pendulum  be  a  lath  (Fig.  47)  sus- 
pended at  its  upper  extremity,  A.     Lengthen  or  shorten 
the  ball  pendulum  till  it  swings  in  the  same  time  as 
the  lath.     Then  the  true  lengths  of  the  two  pendu- 
lums must  be  the  same.    Lay  off  on  the  lath  from  its 
point  of  suspension  a  distance  equal  to  the  distance 
from  the  point  of  suspension  to  the  center  of  the 
ball,  and  this  will  give  the  center  of  oscillation  of  the      B 
lath  pendulum.     This  point,  in  case  the  lath  be  of  FlG-  47> 
uniform  dimensions  and  density  throughout,  will  be  at  C,  or 
at  a  distance  of  two  thirds  the  length  of  the  lath  from  its 
point  of  suspension,  A. 

If  a  weight  (or  bob)  be  attached  to  the  lower  end  of  A  B, 
its  center  of  oscillation  is  moved  lower  and  the  period  of 
vibration  is  lengthened.  If  the  bob  of  a  pendulum  be  raised 
(which  usually  may  be  done  by  turning  a  thuinb-scr-ew  just 
beneath  it),  the  pendulum  is  shortened  and  its  time  of  vibra- 
tion is  decreased. 

63.  Uses  of  the  Pendulum.  The  isochronism  of  the  pendu- 
lum is  utilized  in  the'  measurement  of  time,  i.e.  in  subdividing 
the  solar  day  into  hours,  minutes,  and  seconds.  The  office  of 
the  pendulum  in  clocks  is  to  regulate  the  rate  of  motion  of 
the  works.  The  balance  wheel  replaces  the  pendulum  in 
watches  and  some  clocks. 

One  of  the  most  important  uses  of  the  pendulum  from  a 
scientific  standpoint  is  that  in  determining  the  acceleration 
clue  to  the  force  of  gravitation  at  any  place. 


64  MOLAR   DYNAMICS. 

The  time  of  vibration  is  less  at  a  place  where  the  force  of 
gravitation  is  greater  because  the  accelerating  force  for  the 
same  mass  is  greater,  and  hence  the  pendulum  will  move 
faster. 

Hence,  it  is  apparent  that  by  determining  the  time  of 
vibration  of  a  pendulum  of  the  same  length  at  different 
distances  from  the  center  of  mass  of  the  earth  (e.g.  at  the 
top  and  bottom  of  a  mountain,  or  at  sea  level  at  different 
latitudes),  the  relative  value,  of  g  at  these  places,  i.e.  the 
acceleration  produced  by  gravitation,  may  be  ascertained. 

At  the  poles  of  the  earth  the  length  of  a  seconds  pendulum  is  99.62  cm. 
and  g  =  983.2cm.  per  second.  At  the  equator,  I  =  99.10  cm. ;  g  =  978.1  cm. 
per  second. 

EXERCISES. 

1.  (a)  What  is  the  length  of  a  pendulum  that  beats  half-seconds  ? 
(6)  Quarter-seconds  ?     (c)  That  makes  one  vibration  in  two  seconds  ? 
(d)  That  makes  two  vibrations  per  minute  ? 

2.  State  the  proportion  that  will  give  the  number  of  vibrations  per 
minute  made  by  a  pendulum  40  cm.  long. 

3.  How  will  the  periods  of  vibration  compare  in  the  case  of  two  pen- 
dulums whose  lengths  are,  respectively,  4  feet  and  49  feet  ? 

4.  Two  pendulums  make,  respectively,  50  and  70  vibrations  per  min- 
ute.    Compare  their  lengths. 

5.  How  long  must  a  pendulum  be  to  make  one  vibration  in  5  seconds 
in  Boston  ? 

6.  One  pendulum  is  20  inches  long,  and  vibrates  four  times  as  fast  as 
another.     How  long  is  the  other  ? 

7.  (a)  What  effect  on  the  time  of  vibration  of  a  pendulum  has  the 
weight  of  its  bob  ?    (6)  What  effect  has  the  length  of  the  arc  ?    (c)  What 
affects  the  time  of  vibration  of  a  pendulum  ? 

8.  How  can  you  quicken  the  vibration  of  a  pendulum  threefold  ? 

9.  A  clock  loses  time,     (a)  What  change  in  the  pendulum  ought  to 
be  made  ?     (6)  How  would  you  make  the  correction  ? 

10.  Two  pendulums  are  4  and  9  feet  long,  respectively.     While  the 
short  one  makes  one  vibration,  how  many  will  the  long  one  make  ? 

11.  What  is  the  time  of  vibration  of  a  pendulum  (39.09  -f  4  =)  9.77 
inches  long  ? 


GRAVITATION   IS    UNIVERSAL.  65 

12.  The  number  of  vibrations  made  by  a  given  pendulum  in  a  given 
time  varies  as  the  square  root  of  the  force  of  gravity.     Force  of  gravity 
at  any  place  is  expressed  by  the  value  of  g  (i.  e.  by  the  acceleration  which 
it  produces).     If  at  a  certain  place  a  pendulum  39.09  inches  long  make 
3600  vibrations  in  an  hour,  and  the  value  of  g  be  32.16  feet,  what  is  the 
acceleration  at  a  place  where  the  same  pendulum  makes  3590  vibrations 
in  the  same  time  ? 

13.  A  pebble  is  suspended  by  a  thread  2  feet  long  ;  required  the  num- 
ber of  vibrations  it  will  make  in  a  minute. 


SECTION   X. 
GRAVITATION. 

64,  Gravitation  is  Universal,     We   know  that  there  is  a 
stress  between  the  earth  and  all  bodies  on  or  near  it,  and  we 
have  learned  to  call  this   the   weight  of  bodies.     Sir  Isaac 
Newton  was  the  first  to  show  that  this  stress  is  not  limited 
to  the  earth  and  terrestrial  bodies,  but  exists  between  par- 
ticles separated  by  any  distance,  however  great.    So  that  there 
is  a  stress  between  every  particle  of  'matter  in  the  universe  and 
every  other  particle.     This  mutual  action  is  called  Universal 
Gravitation. 

That  there  is  a  stress  between  the  sun  and  the  earth,  and  the  earth 
and  the  moon,  is  shown  by  their  curvilinear  motions  in  their  orbits. 
Tides  and  tidal  currents  on  the  earth  are  due  to  the  stress  between  the 
sun  and  the  moon  and  the  masses  of  water  on  the  earth's  surface. 

65.  Law  of  Gravitation,     The    Law   of    Universal  Gravi- 
tation is  as  follows  : 

The  gravitation  stress  between  every  two  particles  of  matter  in 
the  universe  varies  directly  as  the  product  of  their  masses,  and 
inversely  as  the  square  of  the  distance  between  them. 

If  the  masses  of  two  bodies  be  represented  by  m  and  m',  the  distance 
between  their  centers  of  mass  by  d,  and  the  gravitation  stress  by  gr,  this 

relation  is  expressed  mathematically  thus :  g  <x  (varies  as)  ~p~*     For 


66  MOLAR   DYNAMICS. 

example,  if  the  mass  of  either  body  be  doubled,  the  product  (mm')  of  the 
masses  is  doubled,  and  consequently  the  stress  is  doubled.  If  the  dis- 
tance between  their  centers  of  mass  be  doubled,  then  (  —  =  -  \  the  stress 
becomes  one  fourth  as  great. 

66,  Law  of  Weight.  The  weight  of  a  body  at  or  above  the 
surface  of  the  earth  varies  inversely  as  the  square  of  the  dis- 
tance from  the  center  of  mass  of  the  earth. 

Since  the  earth  is  not  a  perfect  sphere,1  it  follows  from  the  law  that 
the  weight  of  the  same  body  differs  at  different  places  on  the  earth's  sur- 
face. Its  loss  of  weight  in  being  transported  from  the  poles  to  the  equa- 
tor, due  to  this  increase  of  distance  from  the  center  of  mass  of  the  earth, 
is  estimated  to  be  ^  J-F  of  its  weight  at  the  poles.  But  we  have  previously 
seen  (p.  58)  that  the  tangential  tendency  at  the  equator  diminishes  the 
weight  of  a  body  2^9-  Now  in  consequence  of  difference  in  distance 
from  the  center  of  mass  of  the  earth  and  difference  in  velocity  due  to  the 
earth's  rotation,  a  body  weighs  at  the  equator  3-£T  +  ^$9  =  T-^  less  than 
at  the  poles. 

We  infer  from  the  law  of  gravitation  that  a  body  weighs  more  at  the 
earth's  surface  than  above  it ;  in  other  words,  bodies  become  lighter  as 
they  are  raised  above  the  earth's  surface.  But  since  the  force  diminishes 
as  the  square  of  the  distance  from  the  center  (not  from  the  surface)  of  the 
earth,  and  as  the  surface  is  about  4000  miles  from  the  center  of  mass, 
the  diminution  for  a  few  miles  or  for  any  distance  which  we  are  able  to 
raise  bodies  is  scarcely  perceptible  ;  hence,  in  all  commercial  transactions 
we  may,  without  important  error,  buy  and  sell  as  if  the  weighing  always 
took  place  at  the  same  distance  from  the  center  of  mass  of  the  earth,  in 
which  case  mass  is  strictly  proportional  to  weight. 

EXERCISES. 

1.  (a)    Which    is  independent  of    mass,    weight    or    acceleration  ? 
(6)  Which  varies  as  the  mass  ? 

2.  Why  does  a  100-lb.  iron  ball  fall  with  no  greater  acceleration  than 
a  1-lb.  ball  of  the  same  material  ? 

3.  (a)  Which  falls  with  greater  acceleration  in  the  air,  an  iron  ball 
or  a  wax  ball  ?     Why  ?     (b)  How  would  their  accelerations  compare  in  a 
vacuum  ?     (c)  Is  acceleration  independent  of  kind  of  matter  ? 

1  The  earth  is  a  spheroid,  its  polar  diameter  being  about  43  kilometers  (nearly  27 
miles)  shorter  than  its  equatorial  diameter, 


WORK. ENERGY.  67 

4.  If  the  earth's  mass  were  doubled  without  any  change  of  volume, 
how  would  the  change  affect  your  weight  ? 

5.  On  what  principle  may  you  determine  that  the  mass  of  one  body 
is  ten  times  the  mass  of  another  body  ? 

6.  How  many  times  must  you  increase  the  distance  between  the  cen- 
ters of  mass  of  two  bodies  in  order  that  the  gravitation  stress  between 
them  may  become  one  fourth  as  great  ? 

7.  (a)  If  a  body  on  the  surface  of  the  earth  be  4000  miles  from  the 
center  of  mass  of  the  earth,  and  weigh  at  this  place  100  Ibs. ,  what  would 
the  same   body  weigh  if  it  were   taken  4000  miles  above  the  earth's 
surface?     (6)  What  2000  miles  above  the  earth?     (c)  What  100  miles 
above  the  earth  ? 

8.  If  at  sea  level  in  Boston  g  =  980.4  cm.,  what  is  the  value  of  g  at  a 
point  5  miles  above  sea  level  ? 

9.  What  retains  the  planets  in  their  orbits  ? 

10.  If  there  were  but  one  body  of  matter  in  existence,  (a)  would  it 
have  weight  ?     (6)  Would  it  have  mass  ? 

11.  What  is  the  character  of  the  motion  produced  by  a  constant  force 
acting  on  a  free  body  ? 

SECTION   XI. 
WORK,    ENERGY,    AND   POWER. 

67,  Work.     Whenever  a  force  causes  a  change  of  motion 
or  maintains  motion  against  resistance,  it  is  said  to  do  work. 
A  force  to  do  work  must  effect  a  change  of  position.     Force 
and  space  are  essential  conditions  of  work.     An  unbalanced 
force  always  does  work,  inasmuch  as  it  always  causes  a  change 
of  motion. 

The  body  that  moves  another  body  is  said  to  do  work  upon  it ; 
dad  the  body  moved  is  said  to  have  work  done  upon  it. 

When  the  heavy  weight  of  a  pile  driver  is  raised,  work  is  done  upon 
it :  when  it  descends  and  drives  the  pile  into  the  earth,  work  is  done  upon 
the  pile,  and  the  pile  in  turn  does  work  upon  the  matter  in  its  path. 

68.  Energy.      The   energy   of   a    body   is   its   capacity  for 
doing  work.     It  is  measured  by  the  quantity  of  work  which 
the  body  is  capable  of  doing.     The  work  done  by  a  body,  or 


68  MOLAR   DYNAMICS. 

done  on  a  body,  is  a  measure  of  its  loss  or  gain  of  energy  ; 
hence,  the  unit  of  work  is  also  the  unit  of  energy. 

The  act  of  doing  work  either  consists  in  a  transfer  of  energy 
from  the  body  doing  work  to  the  body  on  which  work  is  done, 
as  when  the  wind  propels  a  vessel,  or  it  consists  in  a  trans- 
formation of  one  kind  of  energy  into  another  kind.  When  the 
pile  driver  strikes  the  pile  and  the  pile  is  forced  into  the 
earth,  a  part  of  the  energy  in  each  act  is  transformed  into 
heat,  which  we  shall  learn,  farther  on,  is  molecular  energy. 
Work,  therefore,  may  be  denned  as  the  act  of  transmitting  or 
transforming  energy. 

69.  Kinetic  and  Potential  Energy.  Every  moving  body 
can  impart  motion,  therefore  it  can  do  work  upon  another 
body  ;  hence,  every  moving  body  possesses  energy.  The  energy 
which  a  body  possesses  in  consequence  of  its  motion  is  called 
kinetic  energy. 

When  a  body  is  projected  upward  its  kinetic  energy  dimin- 
ishes as  it  rises  and  finally  becomes  nil,  but  it  is  not  lost,  for 
it  reappears  as  the  body  falls.  Its  energy  becomes,  while 
rising,  stored  up  in  virtue  of  its  higher  position.  Energy  in 
store,  i.e.  not  in  an  active  state,  is  called  potential  energy.  It 
is  the  capacity  for  doing  work  possessed  by  a  mass  in  virtue 
of  its  position  being  'such  that  it  is  possible  for  it  to  move,  and 
in  virtue  of  the  existence  of  a  stress  which  tends  to  move  it. 
Hence,  it  is  convertible  into  kinetic  energy  without  the  agency 
of  any  additional  work  except  that  of  removing  obstacles 
to  the  conversion.  Potential  energy  implies  a  tendency  to 
motion,  as  truly  as  kinetic  energy  implies  motion. 

Illustrations  of  energy  in  the  potential  state  : 

A  stone  lying  on  the  ground  is  devoid  of  energy.  Raise  it  and  place 
it  on  a  shelf  ;  in  so  doing  you  perform  work  upon  it.  As  you  look  at  it 
lying  motionless  upon  the  shelf,  it  appears  as  devoid  of  energy  as  when 
lying  on  the  earth.  Attach  one  end  of  a  cord  to  it  and  pass  it  over  a 
pulley,  and  wind  a  portion  of  the  cord  around  the  shaft  connected  with  a 


ENERGY   OF   CHEMICAL   SEPARATION.  69 

sewing  machine,  lathe,  or  other  convenient  machine.  Suddenly  withdraw 
the  shelf  from  beneath  the  stone.  The  stone  moves  ;  it  communicates 
motion  to  the  machinery,  and  you  may  sew,  turn  wood,  etc.,  with  the 
energy  given  to  the  machine  by  the  stone. 

The  work  done  on  the  stone  or  the  energy  transmitted  to  the  stone  in 
raising  it  was  not  lost ;  it  reappeared  while  the  stone  was  descending. 
There  is  a  very  important  difference  between  the  stone  when  lying  on  the 
ground  and  the  stone  when  lying  on  the  shelf ;  the  former  is  powerless 
to  do  work  ;  the  latter  can  do  work.  Both  are  alike  motionless,  and  you 
can  see  no  difference,  except  an  advantage  that  the  latter  has  over  the 
former  in  having  a  position  such  that  it  can  move.  What  gave  it  this 
advantage  ?  Work.  A  body,  then,  may  possess  energy  due  merely  to 
ADVANTAGE  OF  POSITION,  derived  from  work  performed  upon  it. 

We  are  as  much  accustomed  to  store  up  energy  for  future  use  as  to 
store  up  provisions  for  the  winter's  consumption.  We  store  it  when  we 
wind  up  the  spring  or  weight  of  a  clock,  to  be  doled  out  gradually  in  the 
movements  of  the  machinery.  We  store  it  when  we  bend  the  bow, 
condense  air,  or  raise  any  body  above  the  earth's  surface. 

We  see,  then,  that  energy  may  exist  in  bodies  by  virtue  of 
their  actual  motion,  or  it  may  exist  in  bodies  by  virtue  of 
their  having  an  opportunity  and  a  tendency  to  move,  as  in  the 
stone  lying  on  the  shelf.  But  it  should  be  remembered  that 
a  body  does  work  only  when  moving  ;  hence,  the  potential 
energy  of  a  body  must  become  kinetic  before  the  body  can  do 
work. 

70.  Energy  of  Chemical  Separation.  Matter  may  possess 
potential  energy  in  virtue  of  chemical  separation  and  chemi- 
cal affinity,  and  the  potential  energy  is  a  measure  of  the  work 
done  in  effecting  the  separation.  For  example,  the  entire 
value  of  coal  consists  in  its  potential  energy,  which  was 
stored  up  by  the  work  performed  through  the  agency  of  the 
sun's  energy  in  separating  the  carbon  of  carbon  dioxide  from 
the  oxygen.  Gunpowder  possesses  potential  energy  sufficient 
to  do  a  quantity  of  work,  e.g.  in  blasting,  which  would  require 
many  laborers  a  long  time  to  do. 

A  body  possesses  potential  energy  when,  in  virtue  of  work 
done  upon  it,  it  occupies  a  position  of  advantage,  or  its  con- 


70  MOLAR    DYNAMICS. 

stituent  particles  occupy  positions  of  advantage,  so  that  the 
energy  expended  can  be  restored  at  any  time  by  the  return  of 
the  body  to  its  original  position,  or  by  the  return  of  its  particles 
to  their  original  positions. 

71.  Practical  Units  of  Work  and  Energy,     The  practical 
unit  adopted  is  the  work  done  or  energy -imparted  in  raising  1 
pound  through  a  vertical  hight  of  1  foot.     It  is  called  a  foot- 
pound.    The  metric  unit  is  the  work  done  or  energy  imparted 
in  raising  1  k.  a  vertical  hight  of  1  in.,  and  is  called  a  kilogram- 
meter.    The  kilogrammeter  is  equivalent  to  7.2331  foot-pounds. 
Since  the  work  done  in  raising  1  pound  1  foot  high  is  1  foot- 
pound, the  work  of  raising  1  pound  10  feet  high  is  10  foot- 
pounds, which  is  the  same  as  the  work  done  in  raising  10 
pounds  1  foot  high ;  and  the  same,  again,  as  raising  2  pounds 
5  feet  high. 

There  are  many  kinds  of  work  besides  that  of  raising  weights.  But 
since,  with  the  same  resistance,  the  work  of  producing  motion  against  any 
given  resistance  is  independent  of  direction,  it  is  easy,  in  all  cases  in 
which  the  resistance  and  the  space  through  which  the  resistance  is  over- 
come are  known,  to  find  the  equivalent  in  work  done  in  raising  a  weight 
vertically.  By  thus  securing  a  common  standard  for  measurement  of 
work,  we  are  able  to  compare  any  species  of  work  with  any  other.  For  in- 
stance, let  us  compare  the  work  done  in  sawing  through  a  stick  of  wood  by 
a  man  whose  saw  must  move  10  m.  against  an  average  resistance  of  12  k., 
with  that  done  by  a  bullet  in  penetrating  a  plank  to  a  depth  of  2  cm. 
against  an  average  resistance  of  200  k.  Moving  a  saw  10  m.  against 
12  k.  resistance  is  equivalent  to  raising  12  k.  mass  10  m.  high,  or  doing 
120  kgm.  of  work  ;  a  bullet  moving  2  cm.  against  200  k.  resistance  does 
as  much  work  as  is  required  to  raise  200k.  mass  2  cm.  high,  or  200  X  .02 
=  4  kgm.  of  work.  120  -r-  4  =  30  times  as  much  work  done  by  the 
sawyer  as  by  the  bullet. 

72.  Absolute  Units  of  Work.1     If    force    be    measured   in 
dynes,   and  distance    in    centimeters,   the   work  done   is   ex- 

1  The  pupil  will,  perhaps,  be  assisted  by  the  accompanying  diagram  (Fig.  48)  in 
his  first  attempts  to  acquire  and  classify  the  units  of  force,  energy,  and  work  in  the 
several  systems.  In  this  connection  he  should  consult  the  "  Reduction  of  measures 
to  and  from  the  C.  G.  S.  system  "  in  the  Appendix. 


FORMULAS    FOR    CALCULATING. 


71 


pressed  in  a  C.  G.  S.  unit  called  an  erg.  An  erg  is  the  work 
done  or  energy  imparted  by  a  force  of  one  dyne  acting  through 
a  distance  of  one  centimeter. 

Absolute 


Gram 
Gram-centi 
meter  and 
Kilogram 


The  F.  P.  S.  unit  of  work  or  energy  is  the  foot-poundal,  and  is  the 
work  done  or  energy  imparted  by  a  force  of  one  poundal  acting  through 
a  distance  of  1  foot. 

73.  Formulas  for  Calculating  Work  or  Energy  Imparted. 

Force  and  space  (or  distance),  being  essential  conditions  of 
work,  are  necessarily  the  quantities  employed  in  calculating 
work.  A  given  force  acting  through  a  space  of  1  foot  does 
a  certain  quantity  of  work  ;  it  is  evident  that  the  same  force 
acting  through  a  space  of  2  feet  would  do  twice  as  much 
work.  Hence,  the  general  formula  : 

W  =  fs,  (1) 

in  which  f  represents  the  force  employed,  s  the  space  through 
which  the  force  acts,  and  W  the  work  done. 

In  case  a  force  encounters  resistance,  the  magnitude  of  the 
force  necessary  to  produce  motion  varies  with  the  resistance. 
Often  the  work  done  upon  a  body  is  more  conveniently 


72  MOLAR    DYNAMICS. 

determined  by  multiplying  the  resistance  by  the  space  through 
which  it  is  overcome,  and  our  formula  becomes  by  substitution 
of  r  (resistance)  for /(the  force  which  overcomes  it) 

rs  =  W.  (2) 

For  example,  a  ball  is  shot  vertically  upward  from  a  rifle  in  a  vacuum  ; 
the  work  done  upon  the  ball  (by  the  explosive  force  of  the  gunpowder) 
may  be  calculated  by  multiplying  the  average  force  (difficult  to  ascertain) 
exerted  upon  it  by  the  space  through  which  the  force  acts  (a  little  greater 
than  the  length  of  the  barrel)  ;  or  by  multiplying  the  resistance  to 
motion  offered  by  gravity,  i.e.  its  weight  (easily  ascertained),  by  the 
distance  the  ball  ascends. 

Let  us  calculate  the  energy  stored  in  a  bow  by  an  archer  whose  hand, 
in  bending  the  bow  by  pulling  on  the  string,  moves  6  inches  (|  foot) 
against  an  average  resistance  of  20  pounds.  Here  rs  =  20  X  \  =  10  foot- 
pounds of  work  done  upon  the  bow,  or  10  foot-pounds  of  energy  stored 
in  the  bow. 

74.  Formula  for  Calculating  the  Kinetic  Energy  of  a  Body 
when  its  Mass  and  Velocity  are  Known.  Suppose  a  body 
to  have  a  mass  m  and  a  velocity  v ;  it  can  do  a  definite 
quantity  of  work  before  it  is  thereby  brought  to  rest.  If  it 
be  moving  upward,  a  mutual  work  is  performed  by  it  and  by 
the  earth,  consisting  in  each  destroying  the  other's  momentum. 
If  its  velocity  be  such  that  it  will  rise  to  a  hight  s,  then  its 
kinetic  energy  is  such  that  it  will  do  (/  —  my)  m  g  s  absolute 
units  of  work,  or 

Ek  (kinetic  energy)  =  m  g  s.  (1) 

We  may  find,  then,  to  what  vertical  hight  a  body  having 
a  given  velocity  would  rise  if  directed  upward,  and  from 
formula  (1)  determine  its  kinetic  energy  ;  but  a  formula  may 
be  obtained  which  will  give  the  same  result  with  less  trouble  ; 
thus,  substituting  g  for  a  in  the  formula  v  =  at  (p.  11),  we 
have  v  =  gt ;  whence 

«  =  Vor  <.=  ?*. 

9  <f 


ENERGY    CONTRASTED    WITH    MOMENTUM.  73 

Again,  s  =  ^  gt2  ;  substituting  the  value  of  t2  in  this  equation 
we  have 

v2      v2 


Substituting  for  s  in  equation  (1)  its  value  we  have 

m  v2 


(2) 


a  formula  which  will  determine  the  kinetic  energy  of  a  body 
in  absolute  units  when  its  mass  and  velocity  are  known,  since 
the  energy  is  the  same  whatever  be  the  direction  of  the 
motion. 

Hence,  the  kinetic  energy  of  a  body  is  half  the  product  of  its 
mass  by  the  square  of  its  velocity, 

If  the  result  be  desired  in  gravitation  units,  i.e.  in  gram- 
centimeters  or  foot-pounds,  the  number  of  absolute  units  must 
be  divided  by  g,  since  g  ergs  (980)  are  equivalent  to  one 
gram-centimeter,  or  g  foot-poundals  (32.2)  are  equivalent  to 
one  foot-pound. 

75.  Energy  Contrasted  with  Momentum.  It  is  evident 
from  formula  (2)  that  wlien  the  mass  of  a  body  remains  the 
same,  its  energy  is  proportional  to  the  square  of  its  velocity  ; 
ivhile  its  momentum,  as  we  have  learned,  is  proportional  to  its 
velocity.  In  other  words,  the  effect  of  increasing  the  velocity 
of  a  moving  body  would  seem  to  be  to  increase  its  working 
power  much  more  rapidly  than  its  momentum. 

Furthermore,  we  have  seen  (p.  28)  that  momentum  =  M  V 
—  ft  ;  and  again  (p.  71),  W  (work  done)  or  E^  (kinetic  energy 
imparted)  =  fs. 

The  momentum,  then,  imparted  to  a  body  is  the  product 
of  the  force  into  the  time  it  acts  ;  energy  imparted  is  the 
product  of  force  into  the  space  through  which  it  acts.  It  is 
evident,  therefore,  that  iv  hen  time  is  considered,  force  may  be 
'measured  by  the  momentum,  and  when  the  space  is  considered) 


74  MOLAK   DYNAMICS. 


by  the  energy  which  it  imparts.  If  we  know  only  the  momen- 
tum of  a  body,  we  can  tell  how  long  it  would  move  against 
a  given  resistaii3e,  but  not  how  far.  If  we  know  only  the 
kinetic  energy  of  a  body,  we  can  tell  how  far  it  would  move 
against  a  given  resistance,  but  not  how  long. 

The  following  illustration  will  help  to  make  the  distinction  plain  : 
We  realize  that  there  is  an  important  difference  between  the  slow  motion 
of  a  gun's  recoil  and  the  rapid  motion  of  the  bullet  projected  from  it, 
though,  as  we  have  seen,  the  momenta  are  the  same.  By  a  suitable  force 
the  gun  may  be  brought  to  rest  in  one  second,  and  in  that  time  will  move 
(say)  6  inches.  The  same  force  will  in  one  second  bring  the  bullet  to 
rest,  but,  as  may  be  easily  shown  (assuming  the  mass  of  the  gun  and  the 
bullet  to  be,  respectively,  10  pounds  and  1  ounce),  the  bullet  will  have 
moved  about  250  feet.  Hence,  the  bullet  has  a  much  greater  penetrating 
power  than  the  gun. 

A  bullet  moving  with  a  velocity  of  400  feet  per  second  will  penetrate, 
not  twice,  but  four  times  as  far  into  a  plank  as  one  having  a  velocity 
of  200  feet  per  second.  A  railway  train  having  a  velocity  of  20  miles  an 
hour  will,  if  the  steam  be  shut  off,  continue  to  run  four  times  as  far  as  it 
would  if  its  velocity  were  10  miles  an  hour.  The  reason  is  now  apparent 
why  light  substances,  even  so  light  as  air,  exhibit  great  energy  when 
their  velocity  is  great. 


EXERCISES. 

1.  Does  the  energy  expended  in  raising  the  stones  to  their  places  in 
the  Egyptian  pyramids  still  reside  in  the  stones  ? 

2.  What  kind  of  energy  is  that  contained  in  gunpowder  ? 

3.  Can  a  person  lift  himself,  or  put  himself  in  motion,  without  exert- 
ing force  upon  some  other  body  ? 

4.  (a)  Can  a  body  do  work  upon  itself  ?     (6)  Can  a  body  generate 
energy  in  itself,  i.e.  increase  its  own  energy  ? 

5.  (a)  Suppose  that  an  average  force  of  25  pounds  is  exerted  through 
a  space  of  10  inches  in  bending  a  bow,  what  amount  of  energy  will  it 
give  the  bow  ?     (6)  What  kind   of  energy  will  the  bow,  when  bent, 
possess  ? 

6.  (a)  What  amount  of  kinetic  energy  does  a  mass  of  20  pounds, 
moving  with  a  velocity   of  300  feet  per  second,  possess  ?     (6)  What 
amount  of  work  can  the  body  do  ? 


EXERCISES.  75 

7.  How  many  fold  is  the  kinetic  energy  of  a  body  increased  by 
doubling  its  velocity  ? 

8.  How  high  will  1200  foot-pounds  of  energy  raise  100  pounds  ? 

9.  A  force  of  500  pounds  acts  upon  a  body  through  a  space  of  20 
feet.     One  fourth  of  the  work  is  wasted  in  consequence  of  resistances. 
How  much  available  energy  is  imparted  to  the  body  ? 

10.  How  much  energy  is  stored  in  a  body  weighing  1000  pounds,  at 
a  hight  of  200  feet  above  the  earth  ? 

11.  A  horse  draws  a  carriage  on  a  level  road  at  the  uniform  rate  of 
5  miles  an   hour,     (a)  Does  energy   accumulate  ?     (6)  What    kind  of 
energy  does  the  carriage  possess  ?     (c)  Suppose  that  the  carriage  were 
drawn  up  a  hill,  would  energy  accumulate  ?     (d)  What  kind  of  energy 
would  it  possess  when  at  rest  on  the  top  of  the  hill  ?     (e)  How  would 
you  calculate  the  quantity  of  energy  it  possesses  when  at  rest  on  top  of 
the  hill  ?     (/)  Suppose  that  the  carriage  is  in  motion  on  top  of  the  hill, 
what  two  formulas  would  you  employ  in  calculating  the  total  energy  which 


12.  How  much  work  is  done  per  hour  if  80  k.  be  raised  4  m.  per 
minute  ? 

13.  (a)  What  energy  must  be  imparted  to  a  body  weighing  50  g.  that 
it  may  ascend  4  seconds  ?     (b)  How  many  times  as  much  energy  must 
be  imparted  to  the  same  body  that  it  may  ascend  5  seconds  ?     (c)  Why  ? 

14.  Compare  the  momenta,  in  the  two  cases  given  in  the  last  question, 
at  the  instants  the  body  is  thrown. 

15.  How  much  energy  is  stored  in  a  body  which  weighs  50  k.  at  a 
hight  of  80  m.  above  the  earth's  surface  ? 

16.  How  much  kinetic  energy  would  the  same  body  have  if  it  had  a 
velocity  of  100  m.  per  second  ? 

17.  Suppose  it  to  fall  in  a  vacuum,  how  much  kinetic  energy  would 
it  have  at  the  end  of  the  fourth  second  ? 

18.  If  it  should  fall  through  the  air,  what  would  become  of  the  part 
of  the  energy  lost  in  consequence  of  the  resistance  offered  by  the  air  ? 

19.  A  projectile  of  mass  25  k.  is  thrown  vertically  upward  with  an 
initial  velocity  of  29.4  m.  per  second.     How  much  energy  has  it  ? 

20.  What  becomes  of  its  energy  during  its  ascent  ? 

21.  (a)  Compare  the  momentum  of  a  mass  50  k.  having  a  velocity  of 
2  m.  per  second,  with  the  momentum  of  a  body  of  a  mass  50  g.  having  a 
velocity  of  100  m.  per  second.     (6)  Compare  their  energies. 

22.  Which,  momentum  or  energy,  will  enable  one  to  determine  the 
amount  of  resistance  that  a  moving  body  can  overcome  ? 

23.  Explain  how  a  child  who  cannot  lift  30  k.  can  draw  a  carriage 
weighing  150  k. 


76  MOLAR   DYNAMICS. 


24.  How  many  and  what  transformations  take  place  during  a  single 
swing  of  a  pendulum  ? 

25.  What  quantity  of  energy  will  be  expended  if  a  force  of  60  pounds 
move  a  body  a  distance  of  20  feet  ? 

26.  Describe  the  transformations  of  energy  that  take  place  during  a 
single  swing  of  the  pendulum. 

27.  A  blacksmith  raises  a  hammer  and  strikes  an  anvil.     State  all  the 
transformations  of  energy  that  occur. 

28.  How  much  work  is  done  against  gravity  by  a  man  weighing  150 
pounds  in  climbing  a  mountain  a  mile  high  ? 

29.  In  winding  a  clock  a  weight  of  8  pounds  is  raised  a  yard  from  the 
bottom  of  the  clock,     (a)  How  much  energy  is  stored  up  ?     (6)  When 
the  weight  has  fallen  1  foot,  how  much  potential  energy  has  it  left  ? 

(c)  How  much  potential  energy  will  it  have  after  it  has  fallen  2  feet  ? 

(d)  How  has  its  lost  energy  been  expended  ?     (e)  Had  the  weight  fallen 
freely,  what  amount  of  kinetic  energy  and  what  amount  of  potential 
energy  would  it  have  after  falling  2  feet  ? 

30.  Does  the  motion  that   one  body  can  communicate   to   another 
depend  upon  the  momentum  of  the  former,  or  upon  its  energy  ? 

76.  Power.  The  power  (sometimes  called  activity)  of  any 
agent,  e.g.  a  steam  engine,  an  animal,  etc.,  is  the  rate  at  which 
it  does  or  can  do  work,  and  is  measured  by  the  quantity  of 
work  it  either  does  or  can  do  per  unit  of  time,  and  is  deter- 
mined by  the  formula 

.       w  (work) 

P  (power)  =  — }-. (-• 

'       t  (time) 

In  estimating  the  total  quantity  of  work  done,  the  time 
consumed  is  not  taken  into  consideration.  The  work  done  by 
a  hod-carrier  in  carrying  1000  bricks  to  the  top  of  a  building 
is  the  same  whether  he  does  it  in  a  day  or  a  week.  But  in 
estimating  power  or  the,  rate  at  which  the  agent  is  capable  of 
doing  work,  it  is  evident  that  time  is  an  important  element. 
The  work  done  by  a  horse  in  raising  a  barrel  of  flour  20  feet 
is  about  4000  foot-pounds  ;  even  a  mouse  could  do  the  same 
quantity  of  work  in  time,  but  he  has  not  the  power  of  a 
horse. 


EXERCISES.  77 

The  unit  in  which  activity  or  rate  of  doing  work  is  esti- 
mated is  called  (inappropriately)  a  horse-power.  A  horse- 
power is  550  foot-pounds  per  second,  33,000  foot-pounds  per 
minute,  or  1,980,000  foot-pounds  per  hour. 

The  logical  unit  of  power  is  a  unit  of  work  in  a  unit  of 
time,  as  one  erg  per  second.  The  absolute  unit  of  power, 
chiefly  used  in  measuring  electrical  power,  is  the  watt,  or 
10,000,000  ergs  per  second.  A  moderate  estimate  of  man's 
power  is  100  watts. 

1  erg  per  second  =0=  .0000001  watts, 

1  horse-power  =0=  746  watts, 

1  foot-pound  per  minute  =0=  226,043  ergs  per  second. 

EXERCISES. 

1.  For  which  is  a  truck  horse  valued,  his  energy  or  his  power  ? 

2.  Do  we  speak  of  the  power  or  the  energy  of  the  steam  engine  ? 

3.  Which  do  we  apply  to  levers  and  machines  in  general,  power  or 
force  ? 

4.  "  Energy  is  the  power  of  doing  work."     Is  this  true  ? 

5.  Shall  we  say  that  the  power,  or  the  energy,  of  the  horse  is  greater 
than  that  of  man  ? 

6.  How  much  work  can  a  2  horse-power  engine  do  in  an  hour  ? 

7.  (a)  What  quantity  of  work  is  required  to  raise  50  tons  of  coal  from 
a  mine  200  feet  deep  ?     (6)  An  engine  of  how  many  horse-power  would 
be  required  in  order  to  do  it  in  2  hours  ? 

8.  A  car  of  mass  3  tons  is  drawn  by  a  horse  at  a  speed  of  180  feet 
per  minute.    The  index  of  the  dynamometer  to  which  the  horse  is  attached 
stands  at  800  Ibs.     (a)  At  what  rate  is  the  horse  working  ?     (6)  Express 
the  rate  in  horse-power. 

9.  A  dynamometer  shows  that  a  span  of  horses  pull  a  plough  with  a 
constant  force  of  1500  Ibs.     What  power  is  required  to  work  the  plough 
if  they  travel  at  the  rate  of  2  miles  per  hour  ? 

10.  What  horse-power  in  an  engine  will  raise  1,350,000  Ibs.  50  feet  in 
an  hour  ? 

11.  How  long  will  it  take  a  3  horse-power  engine  to  raise  10  tons 
50  feet  ? 

12.  How  far  will  a  2  horse-power  engine  raise  3000  Ibs.  in  10  seconds  ? 


78  MOLAR   DYNAMICS. 

13.  A  force  of  10,000  dynes  acting  through  a  space  of  100  meters  per 
second  furnishes  a  power  of  how  many  watts  ? 

14.  The  wind  moves  a  vessel  with  a  uniform  velocity  of  5  miles  an 
hour  against  a  constant  resistance  of  2000  Ibs.     What  power  is  furnished 
by  the  wind  ? 

15.  If  ^  2  horse-power  engine  can  just  throw  1056  Ibs.  of  water  to  the 
top  of  a  steeple  in  2  minutes,  what  is  the  bight  of  the  steeple  ? 

16.  Supply  the  following  ellipses  by  selecting  appropriate  words  from 
the  following :  viz.  force,  work,  energy,  power.     When  —  acts  through 
space  —  is  performed,  and  —  is  imparted.     The  rate  at  which  —  is  per- 
formed determines  the  —  of  the  agent.     The  —  of  a  bullet  flying  through 
vacant  space.    The  —  of  a  horse.    The  —  of  wind.    The  —  of  a  bent  bow. 
What  —  must  a  bullet  of  mass  1  ounce  have  that  it  may  rise  4  seconds  ? 
What  —  is  consumed  by  a  steamer  in  crossing  the  ocean  ?     What  —  is 
necessary  that  it  may  traverse  300  knots  per  day,  and  what  must  be  the 
average  —  exerted  to  overcome  the  resistances  at  the  required  rate  ? 

17.  It  is  estimated  that  300,000  cubic  feet  of  water  plunge  over  the 
Niagara  escarpment  150  feet  downward  every  second.     What  power  can 
these  falls  furnish  ? 

18.  A  rifle  bullet  whose  mass  is  1  ounce  is  projected  vertically  upward 
with  a  velocity  of  161  feet  per  second.     What  quantity  of  work  does  it 
do  in  rising  against  the  force  of  gravity  ? 


SECTION   XII. 
MACHINES. 

77.  Uses  of  Machines. 

Experiment  1.  Suspend,  as  in  Fig.  49,  a  fixed  pulley,  A,  and  a  mov- 
able pulley,  B.  Let  the  scale-pan  C  counterbalance  the  pulley  B,  so  that 
there  shall  be  equilibrium.  Suspend  from  B  two  balls,  L  L,  of  equal 
weight,  and  suspend  on  the  side  where  the  pan  is  a  single  ball,  K,  equal 
to  one  of  the  former.  The  single  ball  supports  the  two  balls  ;  i.e.  by  the 
use  of  the  machine,  a  force l  of  1  is  enabled  to  balance  a  force  of  2.  So 
far  no  work  is  done.  Place  a  very  small  weight  in  the  pan  ;  this  additional 
weight  destroys  the  balance,  the  balls  L  L  rise,  and  work  is  done  upon  the 
balls. 

1  A  perpetuation  of  the  "  time-honored"  custom  of  calling  the  force  applied  to  a 
machine  power,  and  the  force  exerted  by  the  machine  to  overcome  solne  external 
resistance  weight  —  all  of  which  is  exceedingly  confusing  to  the  pupil  —  is 
indefensible. 


USES    OF   MACHINES. 


79 


As  the  weight  K  plus  a  very  small  weight  causes  the  motion,  we  shall 
regard  this  as  the  force  (f)  ;  and  as  the  weights  L  L  are  the  bodies  moved 
(the  pulleys  and  pan,  being  parts  of  the  machine,  may  be  disregarded),  they 
may  be  regarded  as  the  resistance  (r)  overcome,  or  the  body  on  which 
work  is  done.  Measure  the  respective  distances  through  which  /  acts 
and  r  moves  during  the  same  time:  r  moves 
only  one  half  as  great  a  distance  as  that  through 
which  /  acts  ;  i.e.  if  r  rise  2  feet,  /  must  act 
through  4  feet.  Suppose  that  r  is  2  pounds,  then 
/  is  1  +  pounds.  Now  2  (pounds)  X  2  (feet)  =  4 
foot-pounds  of  work  done  on  r.  Again,  1  + 
(pounds)  X  4  (feet)  =  a  little  more  than  4  foot- 
pounds of  work  (or  energy)  expended. 


It  thus  seems  that,  although  a  machine 
will  enable  a  small  force  to  balance  a 
large  force,  when  work  is  performed  the 
work  applied  to  the  machine  is  greater, 
rather  than  less,  than  the  work  which  the 
machine  transmits  to  the  resistance.    The 
work  applied   is  greater  than  the  work  transmitted  by  the 
amount  of  work  wasted  in  consequence  of  friction  and  other 
resistances.     So  that  by  the  employment  of  a  machine  there  is 
never  a  gain,  but  always  a  loss  of  work. 

What,  then,  is  the  advantage  gained  in  using  this  machine  ? 
Suppose  that  r  is  400  pounds,  and  that  the  utmost  force  that 
a  man  can  exert  is  a  little  more  than  200  pounds.  Then 
without  the  machine  the  services  of  two  men  would  be  required 
to  move  the  resistance  ;  whereas  one  man  can  move  it  with  a 
machine,  although  he  will  be  obliged  to  move  twice  as  far  as 
the  resistance  moves,  a  matter  of  little  consequence  in  com- 
parison with  the  advantage  of  being  able  to  do  the  work  alone. 
The  advantage  gained  in  this  instance  seems  to  be  one  of 
convenience.  Men,  however,  are  accustomed  to  speak  of  it 
as  "a  gain  of  force"  (or  more  commonly  and  inaccurately, 
"of  power"),  inasmuch  as  a  small  force  overcomes  a  large 
resistance. 


80 


MOLAR   DYNAMICS. 


Experiment  2.  If,  instead  of  applying  the  small  additional  weight  to 
the  pan,  it  be  suspended  from  one  of  the  balls  L  L,  the  weight  of  these 
balls,  together  with  the  additional  weight,  becomes  the  cause  of  motion, 
and  K  is  the  resistance.  In  this  case  there  is  a  loss  of  force,  because  the 
force  employed  is  greater  than  the  force  overcome.  Measure  the  dis- 
tances traversed,  respectively,  by  K  and  L  L  in  the  same  time.  K  moves 
twice  as  far  as  L  L,  and  of  course  with  twice  the  speed.  There  is  a  gain 
of  speed  at  the  expense  of  force. 

It  thus  appears  that,  if  it  should  be  desirable  to  move  a 
resistance  with  greater  speed  than  it  is  possible  or  convenient 
for  the  force  to  act,  it  may  be  accomplished  through  the 
mediation  of  a  machine,  by  applying  to  it  a  force  propor- 
tionately greater  than  the  resistance.  This  apparatus  is  one 
of  many  contrivances  called  machines,  through  the  mediation  of 
which  force  can  be  applied  to  resistance  more 
advantageously  than  when  it  is  applied  directly 
to  the  resistance. 

At  present  we  deal  with  machines  employed  as  means 
for  transmitting  and  modifying  motion  and  force.  Later 
we  shall  consider  machines  whose  function  is  to  trans- 
form energy,  such  as  the  steam  engine,  dynamo,  etc. 


Some  of  the  many  advantages  derived  from 
the  use  of  machines  are  : 

(1)   They  may  enable  us  to  exchange  intensity 
of  force  for  speed,  or  speed  for  intensity  of  force. 
A  gain  of  intensity  of  force  or  a 
gain  of  speed  is  called  a  mechanical 
advantage. 

(2)  They  may  enable  us  to  employ 
a  force  in  a  direction  that  is  more 
convenient  than  the  direction  in  which  the  resistance  is  to  be 
moved. 

(3)  They  may  enable  us  to  employ  other  forces  than  our  own 
muscular  force  in  doing  work;  e.g.  the  muscular  force  of  ani- 
mals ;  the  forces  of  wind,  water,  steam,  etc. 


FIG.  50. 


GENERAL   LAW    OF    MACHINES.  81 

How  are  the  last  two  uses  illustrated  in  Fig.  50  ?  The  pulleys  em- 
ployed are  called  fixed  pulleys,  i.e.  they  have  no  motion  except  that  of 
rotation.  Is  any  mechanical  advantage  gained  by  fixed  pulleys  ?  What 
is  the  use  of  a  fixed  pulley  ?  Pulley  B  (Fig.  49)  is  a  movable  pulley. 
What  advantage  is  gained  by  means  of  a  movable  pulley  ? 

78.  General  Law  of  Machines.  From  the  experiments  and 
discussion  above  we  derive  the  following  formula  for  machines  : 

fs  =  rs'  +  w,  (1) 

in  which  f  represents  the  force  applied,  and  s  the  distance 
through  which  f  acts  ;  r  represents  the  resistance  overcome, 
and  s'  the  distance  through  which  its  point  of  application 
is  moved;  w  represents  the  wasted  work.  A  machine  in 
which  there  is  no  wasted  work  is  a  perfect  machine.  Such  a 
machine  is  purely  ideal,  as  none  exists.  If  in  our  calcula- 
tions we  regard  a  machine  as  perfect  (though  subsequently 
suitable  allowance  must'  be  made  for  the  wasted  work),  then 
our  formula  becomes  fs  =  rs',  (2) 

whence  r:f::s:s'j  i.e.  the  force  and  the  resistance  vary  in- 
versely as  the  distances  mhich  their  respective  points  of  appli- 
cation move.  In  other  words,  the  ratio  of  the  resistance  to 
the  force  is  the  reciprocal  of  the  ratio  of  the  distances  which 
these  points  move  ;  thus,  if 

r:/=4,  thens':  s  =  J. 

This  law  applies  to  machines  of  every  description  ;  hence  it 
is  called  the  General  or  Universal  Law  of  Machines.  When 
r  is  greater  than  /,  there  is  a  gain  of  intensity  of  force,  and 

r 

-=•  the  ratio  of  gain  of  intensity  of  force.     When  s'  is  greater 


than  s,  there  is  a  gain  of  speed,  and  -  =  the  ratio  of  gain  of 

S 

speed. 

Since  fs}  the  work  done  upon  a  machine,  is  always  greater 
than  rs'}  the  work  transmitted  by  the  machine,  we  infer  that 
no  machine  creates  or  increases  energy.  No  machine  transmits 


82  MOLAR    DYNAMICS. 

more  energy  than  it  receives.  A  machine  may  enable  us  to 
gain  intensity  of  force,  but  not  energy.  By  taking  s  great 
enough, /can  be  made  as  small  as  we  please;  in  this  case  in 
proportion  as  force  is  gained,  time,  distance,  or  speed  is  lost. 

79.  Efficiency  of  Machines.     The  efficiency  of  a  machine  is 
a  fraction,  usually  a  per  cent,  expressing  the  ratio  of  the 
energy  given  out  by  the  machine  and   utilized  to  the  total 
energy   expended   upon    the   machine.      The    limit   of    the 
efficiency  of  a  machine  is  unity,  which  is  the  efficiency  of  an 
"  ideal,"  or  perfect,  machine,  in  which  no  energy  is  lost.     The 
object  of  improvements  in  machines  is  to  bring  their  efficiency 
as  near  to  unity  as  possible. 

For  instance,  if  50  foot-pounds  of  energy  be  expended  on  a  machine, 
and  friction  convert  8  foot-pounds  into  heat,  and  5  foot-pounds  be  lost  in 
consequence  of  the  utilization  of  only  a  component  of  the  working  force, 
so  that  the  machine  is  able  to  give  out  only  37  foot-pounds,  its  efficiency 
is  f ^  =  74  per  cent.  If  the  friction  can  be  reduced  one  half,  and  an  im- 
provement can  be  made  in  the  machine  which  will  render  the  entire 
working  force  effective,  then  there  will  be  wasted  only  4  foot-pounds  of 
energy,  and  its  efficiency  will  be  raised  to  f  §  =  92  per  cent,  and  the  quan- 
tity of  work  which  the  machine  will  accomplish  will  be  increased  in  the 
ratio  of  92 :  74. 

80.  Mechanical  Powers,     Machines, .  however  complicated 
or  complex,  are  largely  composed  of  a  few  simple  machines 
long  known  as  the  "  mechanical  powers."     As  usually  given 
they  are  the  Lever,  Wheel  and  Axle,  Inclined  Plane,  Screw, 
and  Pulley. 

81.  Experiments  with  the  Lever. 

Experiment  3.  Support  a  lever,  as  in  Fig.  51,  so  that  there  shall  be 
unequal  arms.  Move  W  until  the  lever  is  balanced  in  a  horizontal  posi- 
tion. Suspend  (say)  seven  balls  from  the  short  arm  (say)  one  space  from 
the  fulcrum.  Then  from  the  other  arm  suspend  a  single  ball  from  such 
a  place  (in  this  case  seven  equal  spaces  from  the  fulcrum)  that  it  will 
balance  the  seven  balls.  There  is  now  equilibrium  between  the  two  forces. 
Suppose  the  smaller  force  to  be  increased  a  little  and  to  produce  motion, 
what  mechanical  advantage  (i.e.  intensity  of  force  or  speed)  would  be 


EXPERIMENTS  WITH  THE  LEVER. 


83 


FlG'5L 


gained  by  the  use  of  the  machine  ?     What  is  the  ratio  of  gain,  the  small 

additional  force  being  neglected  ?     How  does  this  ratio  compare  with  the 

ratio  between  the  length  of  the 

two   arms?      For   convenience 

we  call  the  distance  of  the  point 

of  application  of  the  force  from 

the  fulcrum  the  force-arm,  and 

the  distance  of  the  resistance 

from  the  fulcrum  the  resistance- 

arm. 

Suppose  the  small  additional   force  to  be  applied  to  the  short  arm, 

what  mechanical  advantage  would  be  gained  ?     What  would  be  the  ratio 

of  gain? 

While  the  general  law  of  machines  (§  78)  is  always  applicable,  its 

application  is  not  always  convenient,  since,  for  example,  it  necessitates 

putting  the  machine  in  motion  in  order  to  measure  s  and  sf  (the  distances 

traversed,  respectively,  by  the 
points  of  application  of  the 
force  and  resistance  in  the 
same  time),  an  operation  which 
would  be  very  difficult  and 
tedious  in  many  cases.  Hence 
a  special  law,  one  in  which  the 
relation  between  the  ratio  of 
gain  and  the  ratio  between 
certain  dimensions  of  the  ma- 
chine is  stated,  is  often  more 
convenient  in  practice.  For 
example,  in  our  experiment 
with  the  lever  we  discover 
that  r:f::  force-arm  :  resist- 
ance-arm, i.e.  the  force  and 
resistance  vary  inversely  as  the 
lengths  of  their  respective  arms. 
Compare  this  special  law  with 
the  general  law.  Place  the  ful- 

FlG  52  crum  at  other  points  in  the 

lever,  and  thereby  vary  the 

length  of  the  arms,  and  verify  by  numerous  experiments  the  special  law 
of  levers. 

Experiment  4.     By  means  of  a  pulley,  D,  so  arrange  that  both  /  and 
r  may  be  on  the  same  side  of  the  fulcrum  (Fig.  52).     First,  place  in  the 


84 


MOLAR   DYNAMICS. 


pan  weights  sufficient  to  produce  equilibrium  in  the  machine  (for  exam- 
ple, in  this  case,  one  ball).  Then  suspend  weights  at  some  point,  as  A, 
and  place  other  weights  in  the  pan  to  counterbalance  these.  Verify  the 
law  of  levers.  If.  A  be  the  resistance,  what  mechanical  advantage  is 
gained  ?  What  is  the  ratio  of  gain  ?  If  B  be  the  resistance,  what  me- 
chanical advantage  is  gained  ? 

82.  Wheel  and  Axle.  The  wheel  and  axle  consists  of  two 
cylinders  having  a  common  axis,  the  larger  of  which  is  called 
the  wheel,  and  the  smaller  the  axle>  as  A  and  C  (Fig.  53).  The 


FIG.  53. 


PIG.  54. 


wheel  may  be  moved  by  the  hand  or  by  a  string  with  a  weight 
attached  to  it.  The  wheel  is  often  replaced  by  a  crank,  as  in 
the  windlass,  or  by  a  spoke,  as  in  the  capstan,  and  is  thus  em- 
ployed in  hoisting  apparatus,  such  as  cranes,  derricks,  etc. 

The  wheel  and  axle  will  be  seen  (Fig.  54)  to  be  only  a  modification  of 
the  lever,  which,  unlike  the  latter,  may  be  continuous  in  its  operation. 
C  is  the  fulcrum,  the  radius  C  A  is  the  force-arm,  and  the  radius  C  B  the 
resistance-arm.  The  laws  pertaining  to  this  machine  are  virtually  the 
same  as  those  of  the  lever.  For  example,  when  the  force  /  is  applied  to 
the  wheel  and  the  resistance  r  is  at  the  axle, 

_ 1  1 

JB  (radius  of  wheel)  '  R'  (radius  of  axle) 


INCLINED    PLANE. 


85 


83.  Inclined  Plane.  Any  plane  surface  not  horizontal  or 
vertical,  known  as  an  inclined  plane,  may  be  used  as  a  simple 
machine  for  gaining  intensity  of  force  ;  e.g.  a  plank  resting 
with  one  end  on  a  cart  body  and  the  other  on  the  ground,  a 
hillside,  or  a  road-grade.  The  gradient  is  the  quantity  of 
rise  per  horizontal  foot,  or  it  is  the  ratio  of  the  vertical  rise  to 
the  horizontal  distance.  , 

When  a  body  is  pressed  against  a  hard,  smooth  surface,  the 
resistance  offered  by  the  surface  is  at  right  angles  to  the 


FIG.  55. 


:  i  if 


surface.  A  body,  e.g.  a  sphere,  may  be  supported  on  a  hori- 
zontal surface,  for  the  weight  acting  downward  is  counter- 
acted by  the  upward  reaction  of  the  plane.  But  since  on  an 
inclined  plane  the  reaction  is  not  vertically  upward,  a  body 
cannot  rest  on  it  without  the  aid  of  another  force. 

The  mechanical  advantage  of  this  machine  depends  on  the 
principle  of  the  resolution  of  a  force  into  its  components.   Let 

*  R  0 

A  B  (Fig.  55)  be  an  inclined  plane  whose  gradient  is  ^  •     Let 

a  be  the  center  of  mass  of  the  weight  W  (technically  called 
the  load).  The  line  of  direction  of  the  load  is  along  the 
vertical  a  o,  but  the  pressure  exerted  upon  the  plane  is  in  the 


86  MOLAR    DYNAMICS. 

direction  a  c,  and  the  reaction  of  the  plane  is  in  the  direction 
c  a.  We  may  take  any  length  along  the  vertical  as  a  b  to 
represent  the  load  W. 

Draw  b  c  parallel  to  A  B  to  meet  a  c.  Complete  the  paral- 
lelogram a  d  b  c  with  a  b  as  its  diagonal.  The  force  a  b  is 
thereby  resolved  into  two  forces,  a  c  representing  the  pressure 
upon  the  plane,  and  a  d  representing  an  unbalanced  force 
tending  to  move  W  along  the  plane  B  A.  It  is  evident  that 
to  produce  equilibrium,  i.e.  to  support  the  body  on  the  plane 
A  B,  a  force  equal  to  a  d,  but  opposite  in  direction,  must  be 
employed.  Now  it  may  be  proved  geometrically  that  the 
triangles  a  d  b  and  B  C  A  are  similar  ;  i.e. 

d  a  :  a  b  :  :  C  B  :  B  A. 

But  d  a  represents  the  force  f  necessary  to  produce  equilib- 
rium, while  a  b  represents  the  load  or  resistance  r\  C  B 
represents  the  hight  7^  and  B  A  the  length  I,  of  the  inclined 
plane.  Therefore, 

f:r::7t:lj  or/  =  -r. 

Hence,  a  given  force  acting  parallel  to  the  direction  of  incli- 
nation of  an  inclined  plane  will  support  a  weight  as  many 
times  greater  than  itself  as  the  length  of  the  inclined  plane 
is  greater  than  its  vertical  hight.  Corollary  :  with  a  given 
length  of  inclined  plane,  the  greater  its  vertical  hight,  i.e.  the 
steeper  it  is,  the  greater  f  must  be. 

84.  The  screw  is  a  variety  of  inclined  plane,  as  may  be  shown  by 
winding  a  triangular  piece  of  paper  around  a  cylinder,  e.g.  a  lead  pencil 
(Fig.  56).  The  hypotenuse  will  form  a  spiral  about  the  cylinder  resem- 
bling the  threads  of  a  screw. 

In  actual  practice  the  screw  consists  of  two  parts  :  (1)  a  convex 
grooved  cylinder,  or  screw,  S  (Fig.  57),  which  turns  within  (2)  a  hollow 
cylinder,  or  nut,  N.  The  concave  surface  of  the  latter  is  cut  with  a 
thread  corresponding  to  the  thread  of  the  screw.  The  force  is  employed 
either  to  turn  the  screw  within  an  immovable  nut,  or  to  turn  the  nut 


THE    SCREW. 


87 


about  a  fixed  screw.     In  either  case  the  force  is  usually  applied  to  a  lever 
or  wheel  fitted  either  to  the  screw  or  to  the  nut. 

During  a  single  rotation  of  the  screw  or  nut,  the  load  or  resistance  is 
moved  a  distance  equal  to  the  vertical  distance  between  the  correspond- 


a— *- 


FIG.  57. 


FIG.  58. 


ing  surfaces  of  two  successive  threads,  usually  termed 
the  pitch  of  the  screw,  as  a  b  (Fig.  58).     Then  in  con- 
formity to  the  universal  law  of  machines 
the  force  is  to  the  resistance  as  the  dis- 
tance between  the  corresponding  surfaces 
FIG.  56.  of  two  successive  threads  is  to  the  circum- 

ference of  the  circle  described  by  the  force. 

EXERCISES. 

1.  (a)  When  is  a  machine  said  to  gain  intensity  of  force  ?     (b)  When 
is  it  said  to  gain  speed  ? 

2.  (a)  How  is  intensity  of  force  gained  by  the  use  of  a  machine  ? 
(b)  How  is  speed  gained  by  the  use  of  a  machine  ? 

3.  (a)  What  is   mechanical   advantage  ?     (6)  Give  a  rule  by  which 


FIG.  59. 

the  mechanical  advantage  that  may  be  gained  by  any  machine  may  be 
calculated. 

4.  Energy  is  applied  to  a  machine  at  the  rate  of  250  foot-pounds 
per  minute,  and  it  transmits  200  foot-pounds  per  minute.     What  is  its. 
efficiency  ? 

5.  (a)  What  advantage  is  gained  by  a  nut-cracker  (Fig.  59)  ?    (b)  What 
is  the  ratio  of  gain  ? 


88 


MOLAR    DYNAMICS. 


6.    (a)  What  advantage  is  gained  by  cutting  far  back  on  the  blades 
of  shears  near  the  fulcrum  (Fig.  60)  ?.    Why  ?     (b)  Should  shears  for 


FIG.  60. 

cutting  metals  be  made  with  short  handles  and  long  blades,  or  the  reverse  ? 
(c)  What  is  the  advantage  of  long  blades  ? 

7.  The  arm  is  raised  by  the  contraction  (shortening  by  muscular 
force)  of  the  muscle  A  (Fig.  61),  which  is  attached  at  one  extremity  to 
the  shoulder  and  at  the  other  extremity,  B,  to  the  fore-arm,  near  the 
elbow,  (a)  When  the  arm  is  used,  as  represented  in  the  figure,  to  raise 


FIG.  61. 


FIG.  62. 


a  weight,  what  kind  of  machine  is  it  ?  (b)  What  mechanical  advantage 
is  gained  by  it  ?  (c)  How  can  the  ratio  of  gain  be  computed  ?  (d)  For 
which  purpose  is  the  arm  adapted,  to  gain  intensity  of  force  or 
speed  ? 

8.  Is  work  done  when  the  moment  of  the  force  applied  to  a  lever  is 
equal  to  the  moment  of  the  resistance  ?     Why  ? 

9.  Suppose  the  screw  in  the  letter-press  (Fig.  62)  to  advance  £  inch 
at  each  revolution,  and  a  force  of  25  pounds  to  be  applied  to  the  circum- 
ference of  the  wheel  b,  whose  diameter  is  14   inches ;   what  pressure 
would  be  exerted  on  articles  placed  beneath  the  screw  ? 

10.  Two  weights,  of  5  k.  and  20  k.,  are  suspended  from  the  ends  of  a 
lever  70  cm.  long,  (a)  Where  must  the  fulcrum  be  placed  that  they 
may  balance  ?  (b)  What  will  be  the  pressure  on  the  prop  ? 


EXERCISES. 


11.  (a)  A  skid  12  feet  long  rests  with  one  end  on  a  cart  at  a  higlit  of 
3  feet  from  the  ground.     What  force  will  roll  a  barrel  of  flour  weighing 
200  pounds  over  the  skid  into  the  cart  ?     (6)  What  amount  of  work  will 
be  required  ? 

12.  (a)  Draw  a  line  to  represent  an  inclined  plane.     Find  what  is  the 
least  force  that  will  prevent  a  ball  weighing  96  pounds  from  rolling  down 
the  plane.     (6)  Find  the  pressure 

which  the  ball  will  exert  upon  the 
plane. 

13.  An  iron  safe  on   trucks, 
weighing  2   tons,    is    prevented 
from  rolling  down  an   inclined 
plane  by  a  force  of  250  pounds. 
What  is  the  ratio  of  the  length 
of  the  plane  to  its  hight  ? 

14.  If  the  circumference  of  an 
axle  (Fig.  63)  be  60  cm.,  and  the 

point  of  application  of  the  force  applied  to  the  crank  travel  240  cm. 
during  each  revolution,  what  force  will  be  necessary  to  raise  a  bucket  of 
coal  weighing  40  k.  ? 

15.  Through  how  many  meters  must  the  force  act  to  raise  the  bucket 
from  a  cavity  10  m.  deep  ? 

16.  The  truck  (Fig.  64)  is  a  lever  ;  the  fulcrum  is  at  the  axis  M  of  the 
wheels.     A  B  represents  the  line  of  direction  of  the  load,  i.e.  the  direction 
in  which  the  resistance  acts  ;  and  C  D  represents  the  direction  in  which 


Fir,.  63. 


FIG.  64. 

a  force  acts  to  produce  equilibrium  in  the  load  in  its  present  position, 
(a)  What  represents  the  force-arm  ?  (6)  What  represents  the  resistance- 
arm  ?  (c)  The  force  required  to  support  the  load  is  what  part  of  the 
load  ?  (d)  Would  greater,  or  less,  force  be  required  if  it  were  applied  at 


90 


MOLAR   DYNAMICS. 


E  instead  of  C  ?    Why  ?     (e)  How  may  the  load  be  supported  without 

any   force   applied    to  the  lever,   the   legs  not   touching   the   ground  ? 

(/)  Would  its  equilibrium  in  this  position  be  stable  or  unstable  ?     Why  ? 

(g)  Suppose  the  feet  F  to  rest  upon  the  ground,  how  would  the  pressure 
of  the  load  be  distributed  between  the  feet 
and  wheels  ?  (h)  Which  is  better  suited  for 
moving  heavy  burdens,  a  wheelbarrow  or  a 
truck  ?  Why  ?  (i)  Suppose  that  C  D  repre- 
sents the  supporting  force  and  C  G  the  force 
employed  in  moving  the  load,  how  would  the 
intensity  and  direction  of  the  single  force 
that  accomplishes  both  results  be  found  ? 

17.  What  must  be  the  diameter  of  a  wheel 
in  order  that  a  force  of  20  pounds  applied  at 
its  circumference  may  be  in  equilibrium  with 
a  resistance  of  600  pounds  applied  to  its  axle, 
which  is  3  inches  in  diameter  ? 

18.  (a)  Where  is  the  fulcrum  in  a  claw- 
hammer (Fig.  65)  ?     (6)  What  is  the  ratio  of  the  mechanical  advantage 
gained  by  means  of  it  ? 

19.  In  its  technical  meaning,  a  "perpetual  motion  machine  "  is  not  a 
machine  that  will  run  indefinitely,  but  a  machine  which  can  do  work 
indefinitely  without  the  expenditure  of  energy.  Show  that  such  a  machine 
is  impossible. 

In  the  arrangement  shown  in  Fig.  66  three 
simple  levers  are  combined  so  as  to  form  one 
compound  lever.  The  supporting  force  is  ap- 
plied at  A  ;  the  resistance  applied  to  this 
simple  lever  at  B  is  identical  with  the  force 
applied  at  A',  and  so  on.  Now 


FIG.  65. 


f=lX 


continuous  product  of  resistance-arms 
continuous  product  of  force-arms 


A  combination  of  levers  similar  to  this 
may  be  seen  in  scales  used  for  weighing  very  FJG  66 

heavy  bodies,  such  as  the  so-called  platform 

"hay-scales,"  in  which  a  comparatively  small  weight  counterbalances 
the  heavy  load. 


Fig.  67  represents  a  train  of  wheels  in  gear.     A  train  of 
wheels  being  analogous  to  a  compound  lever,  the  mechanical 


COHESION    AND    TENACITY. 


91 


advantage  gained  is  obviously  the  ratio  of  the  continued 
product  of  the  radii  of  the  wheels  to  the  continued  product 
of  the  radii  of  the  axles. 

20.  Suppose  the  lengths  of  the 
arms  of  the  several  levers  in  Fig. 

*9  66  bear  the  following  relations  to 
C    each  other  :  5  :  1,  4  :  1,  and  3:1; 
*     what  force  applied  at  A  will  sup- 
port 180  pounds  at  W  ? 

21.  (a)   In   what    sense   may 
machines   be    ' '  labor  -  saving ' '  ? 
(&)  In  what  sense  is  no  machine 
"labor-saving"  ? 

22.  If  the  arms  of  the  lever  of 
a  hydrostatic  press  be  3  feet  and 
\  foot,  and  the  diameters  of  the 
plungers  be  3  inches  and  3  feet, 

a  force  of  50  pounds  will  produce  what  pressure  ? 

23.  Suppose  that  the  radii  of  the  wheels  a,  d,  and  f  (Fig.  67)  are, 
respectively,  20  inches,  16  inches,  and  24  inches,  and  the  radii  of  their 
axles  are,  respectively,  2  inches,  4  inches,  and  6  inches  ;  how  great  advan- 
tage may  be  gained  by  the  compound  machine  ? 


•f 


FIG.  67. 


SECTION   XIII. 

SOME   PROPERTIES    OF    MATTER    DUE   TO   MOLECULAR 
FORCES. 


85.  Cohesion  and  Tenacity.  According  to  the  theory  of 
the  constitution  of  matter  (§  3)  the  molecules  of  every  mass 
are  in  ceaseless  motion,  hitting  and  rebounding  from  one 
another.  This  tends  to  drive  the  molecules  apart.  In  gaseous 
masses  the  molecules  move  without  restraint ;  hence  gaseous 
bodies  always  tend  to  expand. 

In  solids  and  liquids  the  molecules  are  held  under  the  action 
of  a  very  powerful  attractive  force,  called  cohesion,  which  pre- 


92  MOLAR    DYNAMICS. 

vents  their  separation  except  under  the  action  of  considerable 
external  force.  It  is  the  force  which  resists  an  effort  tending 
to  break,  tear,  or  crush  a  body.  The  tenacity  or  tensile  strength 
of  solids  and  liquids,  i.e.  the  resistance  which  they  offer  to  being 
pulled  apart,  is  due  to  this  force.  It  is  usually  greater  in 
solids  than  in  liquids,  and  is  entirely  wanting  in  a  true  gas. 

86.  Elasticity.     Elasticity  is  that  property  in  virtue  of  which 
a  solid  tends  to  recover  its  size  and  shape,  and  a  fluid  its  size, 
after  deformation.     Solids  are  remarkable  for  high  rigidity. 
A  perfectly  rigid  solid  is  one  which,  when  a  force  is  applied 
to  it  in  any  way,  suffers  no  strain  before  breaking.     No  body 
is  absolutely  rigid,  though  some  bodies  are  approximately  so. 
If  the  stress  between  the  molecules  in  opposition  to  the  dis- 
torting force  continue  constant,  regardless  of  the  time  the 
strain  is  kept  up,  and  restore  the  body  to  its  normal  condition 
immediately  on  the  removal  of  the  distorting  force,  without 
any  permanent  strain  or  "  set,"  the  body  is  said  to  be  perfectly 
elastic.     All  fluids  are  perfectly  elastic,  and  a  few  solids  are 
approximately  so,  such  as  ivory,  steel,  and  glass. 

If  a  solid  have  little  or  no  tendency  to  recover  its  size  and  shape  after 
distortion,  it  is  said  to  be  plastic  or  inelastic.  Such  substances  are  putty, 
wet  clay,  and  dough.  A  great  number  of  substances  are  elastic  when 
the  distorting  forces  are  small,  but  break  or  receive  a  "set  "  when  these 
forces  are  too  great.  They  are  said  to  be  elastic  "  within  certain  limits," 
called  the  limits  of  elasticity.  If  strained  beyond  those  limits,  they 
become  more  or  less  plastic.  Hence,  the  springs  of  a  buggy  sometimes 
become  set  from  bearing  a  too  heavy  load,  and  lose  permanently  much 
of  their  elasticity  ;  i.e.  they  become  in  a  degree  plastic. 

87.  Viscosity. 

Experiment  1.  Support  in  a  horizontal  position,  by  one  of  its 
extremities,  a  stick  of  sealing  wax,  and  suspend  from  its  free  extremity 
an  ounce  weight,  and  let  it  remain  in  this  condition  several  days.  At 
the  end  of  the  time  the  stick  will  be  found  permanently  bent.  Should 
an  attempt  be  made  to  bend  the  stick  quickly,  it  will  be  found  to  be 
quite  brittle. 


HARDNESS.  93 

The  experiment  shows  that  sealing  wax  possesses  fluidity, 
freedom  of  motion  of  its  molecules  around  one  another,  in  a 
small  degree.  Eesistance  to  deformation,  due  to  the  friction 
of  the  molecules  of  a  body  in  sliding  over  one  another,  is 
called  viscosity.  Bodies  that  slowly  suffer  continuous  and 
permanent  deformation  under  the  action  of  a  continuous 
stress  are  said  to  be  viscous.  A  lump  of  pitch  in  course  of 
time  loses  its  sharpness  of  outline  and  flows  down  hill  of 
its  own  weight.  It  is  very  viscous.  Cold  molasses  is  quite 
viscous,  but  as  its  temperature  is  raised  its  viscosity  dimin- 
ishes and  it  becomes  more  and  more  plastic  or  mobile.  A 
perfectly  rigid  solid  is  one  of  infinite  viscosity.  A  perfect 
fluid  is  a  fluid  which  possesses  no  viscosity.  Gases  are 
viscous  to  some  extent  and  are  therefore  imperfect  fluids. 

Bodies  surrounded  by  air  have  on  their  surfaces  an  adherent  filin  of 
air.  When  they  move,  this  film  rubs  against  the  surrounding  air,  and 
thus  their  movements  are  retarded  by  friction  in  the  air.  To  the 
viscosity  of  the  air  is  due  in  part  the  retardation  of  the  velocity  of 
falling  bodies. 

88.  Hardness.  Hardness  is  resistance  to  abrasion  or 
scratching. 

To  enable  us  to  express  degrees  of  hardness,  the  following 
table  of  reference  is  generally  adopted  : 

MOHR'S  SCALE  or  HARDNESS. 

1.  Talc.  6.  Orthoclase  (Feldspar). 

2.  Gypsum  (or  Rock-Salt).  7.  Quartz. 

3.  Calcite.  8.  Topaz. 

4.  Fluor-Spar.  9.  Corundum. 

5.  'Apatite.  10.  Diamond. 

By  comparing  a  given  substance  with  the  substances  in  the 
table,  its  degree  of  hardness  can  be  indicated  approximately. 
Thus,  "H=7"  means  that  the  body  is  about  as  hard  as 
quartz. 


94  MOLAR   DYNAMICS. 

89.  Malleability ;  Ductility.    Solids  which  possess  that  kind 
of  fluidity  which  renders  them  susceptible  of  being  rolled  or 
hammered  out  into  sheets  are  said  to  be  'malleable.     Most 
metals  are  highly  malleable.     Gold  may  be  hammered  so  thin 
as  to  be  transparent,  or  to  a  thickness  of  one  three-hundred- 
thousandth  of  an  inch.     Most  substances  that  are  malleable 
are  also  susceptible  of  being  drawn  out  into  fine  threads,  e.g. 
wire  of  different  metals.     Such   substances  are  said   to  be 
ductile.     Platinum  has  been  drawn  into  wire  .000165  inch 
thick,  or  so  fine  as  to  be  scarcely  visible  to  the  unaided  eye. 

90.  Cohesion  in  Liquids.     Clean  glass   is  wet   by  water. 
If  a  glass  plate  be  dipped  into  water  and  then  withdrawn,  a 
layer  of  water  clings  to  the  glass.     When  the'  glass  is  with- 
drawn, water  is  torn  from  water,  and  not  glass  from  water. 
This  shows  that  the  attraction  of  the  molecules  of  water  for 
one  another  is  weaker  than  the  attraction  between  glass  and 
water.     Or  if,  to  save  words,  we  call  the  attraction  between 
the  solid  and  the  liquid  adhesion,1  then  we  may  say  that  the 
cohesion  between  the  molecules  of  the  water  is  weaker  than 
the  adhesion  between  the  glass  and  the  water. 

Clean  glass  is  not  wet  by  clean  mercury,  which  shows  that 
the  adhesion  between  glass  and  mercury  is  not  so  great  as 
the  cohesion  in  mercury.  Generally  speaking,  a  solid  is  wet 
by  a  liquid  when  the  adhesion  of  the  solid  to  the  liquid  is 
greater  than  the  cohesion  of  the  liquid,  and  is  not  wet  when 
the  cohesion  is  greater  than  the  adhesion. 

91.  Tension.     When  a  rubber  band  is  stretched,  it  is  said 
to   be   in   a  state   of   tension,  and  there  exists  between  its 
molecules  a  contractile   or  resilient   stress  which   tends   to 
restore  the  body  to  its  normal  condition.     A  rubber  balloon 
inflated  with  compressed  air  is  in  a  state  of  tension  in  every 
direction. 

1  There  is  no  reason  for  supposing  that  adhesion  is  a  different  force  from 
Cohesion, 


xT 

if      V"   OF  THE 

SURFACE   TENSION.  95 

\     c, 

92.  Surface  Tension  and  Surface  Viscosity.  Every  liquid 
behaves  as  if  a  thin  film  forming  its  external  layer  were  ever 
in  a  state  of  tension,  or  were  exerting  a  constant  effort  to 
contract.  This  superficial  film  is  tough  or  hard  to  break  as 
compared  with  the  interior  mass.  This  property  is  called 
surface  viscosity.  It  is  not  within  the  scope  of  this  book  to 
explain  how  the  molecular  forces  produce  this  result ;  it  must 
suffice  to  call  attention  to  the  peculiar  condition,  with  refer- 
ence to  mutual  attractions,  of  those  molecules  which  compose 
the  surface  film.  In  the  interior  of  a  liquid  body  each  mole- 
cule is  surrounded  by  other  similar  molecules,  and  is  acted 
upon  equally  in  all  directions.  At  a  free  surface  the  mole- 
cules can  be  acted  upon  only  by  others  lying  internal  to  them  ; 
the  outcome  of  this  condition  is  that  it  tends  to  reduce  the 
free  surface  to  the  least  possible  area.  This  tendency  of  a 
liquid  surface  to  contraction  means  that  it  acts  like  an  elastic 
membrane,  equally  stretched  in  all  directions,  and  by  a  con- 
stant tension. 


Experiment  2.  Form  a  soap-bubble  at  the  orifice  of  the  bowl  of  a 
tobacco-pipe,  and  then,  removing  the  mouth  from  the  pipe,  observe  that 
tension  of  the  two  surfaces  (exterior  arid  interior)  of  the  bubble  drives 
out  the  air  from  the  interior  and  finally  the  bubble  contracts  to  a  flat 
sheet.  The  viscosity  of  a  free  surface  of  a  solution  of  soap  in  water  is 
greater  than  that  of  pure  water ;  hence,  its  greater  adaptability  to  the 
formation  of  bubbles. 

As  a  consequence  of  surface  tension,  every  body  of  liquid  tends  to 
assume  the  spherical  form,  since  the  sphere  has  less  surface  than  any  other 
form  having  equal  volume.  In  bodies  of  large  mass  the  distorting  forces 
due  to  gravity  are  generally  sufficient  to  disguise  the  effect ;  but  in  bodies 
of  small  mass,  e.g.  drops  of  liquids,  and  soap-bubbles,  it  is  apparent. 

93.  Capillary  Phenomena.  If  a  glass  rod  be  thrust  vertically  into 
water  so  as  to  leave  a  part  projecting  into  the  air,  the  surface  of  the  water 
does  not  meet  the  rod  at  right  angles,  but  is  turned  up  so  as  to  form  a 
very  small  angle  with  the  surface  of  the  glass,  as  A  C  B  (Fig.  68).  Here 
the  three  substances,  water,  glass,  and  air,  are  brought  in  contact,  and 


96 


MOLAR    DYNAMICS. 


there  are  in  operation  a  triplet  of  tensions  (for  the  surfaces  of  all  bodies 
tend  to  contract),  the  resultant  of  which  is  a  force  which  pulls  the  water 
up  against  the  glass  wall.  On  the  other  hand,  if  mercury,  glass,  and  air 
be  brought  in  contact,  the  relation  between  the  triplet  of  forces  becomes 


FIG.  68. 


FIG. 


FIG.  70. 


FIG.  71. 


so  changed  as  to  cause  the  mercury  to  meet  the  glass  at  a  very  large 
angle,  about  135°. 

If  glass  tubes  (Fig.  69)  of  capillary  (hair-like)  bore  be  thrust  into 
water,  the  water  will  rise  in  the  bores  considerably  above  the  general  level 
outside.  If  similar  tubes  (Fig.  70)  be  thrust  into  mercury,  the  mercury 
within  the  bores  will  be  depressed  below  the  surface  outside.  Phe- 
nomena of  this  kind  are  called  capillary  phenomena.  The  surfaces  of  the 
liquids  inside  the  bores  are  curved,  the  surface  of  water  being  concave 
and  that  of  mercury  convex.  The  size  of  the  bores  of  the  tubes  is 
greatly  exaggerated  in  order  to  show  this  more  plainly.  The  concavity 


CAPILLAKY    PHENOMENA. 


9T 


and  convexity  of  these  interior  surfaces  are  a  necessary  consequence  of 
the  angles  of  contact  with  which  these  liquids  meet  glass. 

It  remains  to  explain  the  elevation  and  depression  of  the  column  of 
liquid  in  the  tube.  This  may  be  done  in  part  by  analogy.  Let  A  B 
(Fig.  71)  represent  a  clothesline  suspended  slackly  between  two  posts. 
From  this  line  hang  by  strings  small  stones,  a,  b,  c,  etc.  If  the  hempen 
line  become  wet,  as  in  a  rain,  it  contracts  and  straightens,  as  shown  by  the 
dotted  line  A  B.  In  other  words,  the  contractile  force  which  is  exerted 
obliquely  (e.g.  n  m,  Fig.  71)  is  resolvable  into  two  forces,  one  of  which  is 
horizontal  and  the  other  is  vertically  upward  ;  the  latter  tends  to  elevate 
the  stones.  In  a  similar  manner  the  curved  surfaces  of  water  and  mer- 
cury tend  to  contract  and  become  flat.  In  the  case  of  the  water  surface 
(which  is  concave)  the  contractile  force  tends  to  elevate  the  pendent  liquid  ; 
but  in  the  case  of  the  mercury  surface 
(which  is  convex)  the  tendency  is  to  produce 
depression.  On  the  nature  of  the  curvature 
depends  the  direction  in  which  the  con- 
tractile force  acts  on  the  pendent  liquid. 
Now  it  is  evident  that  water  will  be  drawn 
up  by  this  contractile  force  until  the  weight 
of  the  column  balances  this  force ;  and 
mercury  will  be  depressed  until  the  force 
is  balanced  by  the  pressure  of  the  mercury 
outside  the  tube.  Capillary  phenomena 
are,  therefore,  phenomena  of  surface  tension.  The  phenomena  of  capil- 
lary action  are  well  shown  by  placing  various  liquids  in  U-shaped  glass 
tubes  having  one  arm  reduced  to  a  capillary  size,  as  A  and  B  in  Fig.  72. 
Mercury  poured  into  A  assumes  convex  surfaces  in  both  arms,  but  does 
not  rise  as  high  in  the  small  arm  as  it  stands  in  the  large  arm.  Pour 
water  into  B,  and  all  the  phenomena  are  reversed.  Fig.  73  shows  the 
forms  that  the  surfaces  of  water  and  mercury  take  when  contained  in  the 
same  glass  tube. 

94.  Laws  of  Capillary  Action.     The  following  laws  may  be 
verified  by  experiment  : 

I.    Liquids  rise  in  tubes  when  they  wet  them,  and  are  de- 
pressed when  they  do  not. 

II.    The  elevation  or  depression  varies  inversely  as  the  diame- 
ter of  the  bore. 


FIG.  72. 


FIG.  73. 


CHAPTER   III. 
DYNAMICS    OP    FLUIDS. 


SECTION  I. 

TRANSMISSION   OF    PRESSURE. 

95,  Law  of  Hydrostatic  and  Pneumatic  Transmission  of 
Pressure.  That  branch  of  science  which  treats  of  liquids  in  a 
state  of  equilibrium  or  rest  is  called  hydrostatics  ;  that  branch 
which  treats  of  liquids  in  motion  is  called  hydrokinetics  ; 
and  that  branch  which  treats  of  the  dynam- 
ics of  air  and  other  gases  is  called  pneu- 
matics. With  the  exception  of  phenomena 
occasioned  by  difference  in  compressibility 
and  expansibility,  liquids  and  gases  are 
subject  to  the  same  laws  and  may  be  treated 
together,  in  so  far  as  they  are  alike,  under 
the  common  term  fluid. 

Experiment  1.  Fill  the  glass  globe  and  cylinder 
(Fig.  74)  with  water,  and  thrust  the  piston  into  the 
cylinder.  Jets  of  water  will  be  thrown  not  only 
from  that  aperture,  A,  in  the  globe  toward  which  the 
piston  moves  and  the  pressure  is  exerted,  but  from 
FIG.  74.  all  the  apertures. 

It  thus  appears  not  only  that  external  pressure  is  exerted 
upon  that  portion  of  the  liquid  that  lies  in  the  path  of  the 
force,  but  that  it  is  transmitted  equally  to  all  parts  and  in  all 
directions. 

When  pressure  is  exerted  upon  a  solid,  on  account  of  its 
rigidity  it  is  incapable  of  transmitting  the  pressure  .in  other 
directions  than  that  in  which  it  is  pressed,  But  fluids,  on 


TRANSMISSION    OF   PRESSURE. 


99 


account  of  the  mobility  of  their  molecules,  are  incapable  of 
resisting  a  change  of  shape  when  acted  upon  at  any  point  by 
a  force,  and  hence  any  force  applied  to  a  fluid  body  must  be 
transmitted  by  the  fluid  in  every  direction.  Consequently, 
every  portion  of  the  interior  walls  of  the  containing  vessel 
with  which  the  fluid  is  in  contact  is  subjected  to  pressure. 

A  pressure,  exerted  on  a  fluid  enclosed  in  a  vessel  is  trans- 
mitted undiminished  to  every  part  of  that  vessel ;  and  the  total 
pressure  exerted  on  the  interior  of  the  vessel  is  equal  to  the  area 
of  the  interior  multiplied  by  the  pressure  per  unit  of  area. 

The  pressure  exerted  by  a  fluid  upon  the  vessel  containing 
it  is  normal  to  the  walls  of  the  vessel.  Fluid  pressure  is 
expressed  by  stating  the  force  exerted  on  a  unit  area,  as 
2  Ibs.'  per  sq.  in.,  5  g.  per  cm.2,  etc. 

Experiment  2.  Fig.  75  represents  a  section  of  an  apparatus  called 
(from  the  number  of  uses  to  which  it  may  be  put)  the  seven-in-one 
apparatus.  A  is  a  hollow  cylinder  closed  at  one  end.  B  is  a  tightly. 


FIG.  75.  FIG.  76. 

fitting  piston  which  may  be  pushed  into  or  drawn  out  of  the  cylinder  by 
the  detachable  handle  C  when  screwed  into  the  piston.  D  is  another 
handle  permanently  connected  with  the  closed  end  of  the  cylinder.  E  is  a 
nipple,  opening  into  the  space  below  the  piston.  To  this  may  be  attached 
a  thickwalled  rubber  tube  F.  G  is  a  stop-cock,  and  H  is  a  funnel,  either 
of  which  may  be  inserted  at  will  into  the  free  end  of  the  tube. 

Support  the  seven-in-one  apparatus  with  the  open  end  upward,  force 
the  piston  in,  place  on  it  a  block  of  wood,  A  (Fig.  76),  and  on  the  block  a 


100 


MOLAR   DYNAMICS. 


heavy  weight.  Attach  one  end  of  the  rubber  tube  B  (12  feet  long)  to  the 
apparatus,  and  insert  a  funnel,  C,  in  the  other  end  of  the  tube.  Raise  the 
latter  end  as  high  as  practicable,  and  pour  water  into  the  tube.  Explain 
how  the  few  ounces  of  water  standing  hi  the  tube  can  exert  a  pressure  of 

many  pounds  on  the  piston,  and  cause 
it  to  rise  together  with  the  burden  that 
is  on  it. 


Experiment  3.     Remove  the  water 
from  the  apparatus,  place  on  the  piston 
a  16-pound  weight,  and  blow  (Fig.  77) 
FlG  yj  from   the   lungs   into    the    apparatus. 

Notwithstanding  that  the  actual  push- 
ing force  exerted  through  the  tube  by  the  lungs  probably  does  not  exceed 
a  few  ounces,  the  slight  increase  of  pressure  caused  thereby,  when  exerted 
upon  the  (about)  26  square  inches  of  surface  of  the  piston,  causes  it  to 
rise  together  with  its  burden. 

96.  The  Hydrostatic  Press.     Closely  allied  to  the  seven-in- 
one  apparatus  is  the  hydrostatic  press.     Water  drawn   from 


FIG.  78. 


a  reservoir.,  A  (Fig.  78),  by  a  suction  and  force-pump  worked 
by  a  lever;   B;  is  forced  along  the  tube  C  into  the  cylinder 


101 

M.  This  cylinder  contains  a  plunger,  P,  which  works  water- 
tight in  the  collar  F.  The  plunger  carries  a  plate,  G,  upon 
which  are  placed  objects  to  be  pressed.  The  water  forced 
into  the  cylinder  exerts  upon  the  plunger  a  total  upward 
pressure  which  is  as  many  times  greater  than  the  downward 
pressure  exerted  upon  the  liquid  through  the  plunger  H  as 
the  area  of  the  cross  section  of  the  plunger  P  is  times  greater 
than  the  area  of  the  cross  section  of  the  plunger  H.  To  obtain 
the  entire  theoretical  gain  of  force  that  may  be  obtained  by 
this  machine  the  ratio  of  the  cross  sections  of  the  plungers 
is  multiplied  by  the  ratio  of  the  two  arms  of  the  lever  B. 

The  pressure  that  may  be  exerted  by  these  presses  is  enormous.  The 
hand  of  a  child  can  break  a  strong  iron  bar.  But  observe  that,  although 
the  pressure  exerted  is  very  great,  the  upward  movement  of  the  plunger 
P  is  very  slow.  In  order  that  the  plunger  P  may  rise  1  cm. ,  the  plunger 
H  must  descend  as  many  centimeters  as  the  area  of  the  cross  section  of  P 
is  times  the  area  of  the  cross  section  of  H.  The  disadvantage  arising 
from  slowness  of  operation  is  insignificant,  however,  when  we  consider 
the  great  advantage  accruing  from  the  fact  that  one  man  can  produce  as 
great  a  pressure  with  the  press  as  several  hundred  men  can  exert  without 
it.  The  modern  engineer  finds  it  a  most  efficient  machine  whenever 
great  resistances  are  to  be  moved  through  short  distances. 

97.  Pascal's  Principle,  Fluids  exert  pressure  due  to  their 
weight.  Imagine  a  vessel  filled  with  shot;  the  upper  layer  of 
shot  will  press  upon  the  layer  next  beneath  with  a  force  equal 
to  its  weight,  the  second  upon  the  third  with  a  force  equal  to 
the  sum  of  the  weights  of  the  first  two,  and  so  on.  You  there- 
fore conclude  that  the  pressure  exerted  upon  the  successive 
layers  will  be  exactly  proportional  to  their  depths.  In  like 
manner  and  for  the  same  reason  the  pressure  at  different  points 
in  a  liquid  is  proportional  to  the  depth. 

Since  shot  possess  a  certain  degree  of  mobility  or  freedom 
of  motion  around  one  another,  their  weight  will  cause  to  some 
extent  a  lateral  pressure  against  one  another  and  against  the 
walls  of  the  containing  vessel.  In  consequence  of  the  extreme 


102 


MOLAR   DYNAMICS. 


mobility  of  the  molecules  of  fluids  the  downward  pressure  due 

to  gravitation  at  any  point  in  a  fluid  gives  rise  to  an  equal 

pressure  at  that  point  in  all  directions.     Hence  the  so-called 

Pascal's  principle:  At 

any  point  in  a  fluid   ^^%^= 

at  rest  the  pressure  is 

equal  in  all  directions.   3|l33^i±El?=p±5 


FIG.  79. 


(Fig.   79),  represent  im- 
aginary surfaces,  and  the 

arrow-heads  the  direction 

of    pressure    exerted    at 

points  in  these  surfaces  at  equal  depths  in  a  liquid.    The  pressures 

exerted  at  these  several  points  are  equal. 

The  truth  of  this  principle  is  obvious,  for  if  there  be  any  inequality  of 

pressure  at  any  point,  the  unbalanced  force  will  cause  particles  at  that 

point  to  move,  which  is  contrary  to 
the  supposition  that  the  fluid  is  al 
rest.  Conversely,  when  there  is  mo- 
tion in  a  body  of  fluid  it  is  evidence 
of  an  inequality  of  pressure. 


98,  Methods  of  Calculating  Liquid 
Pressure.  Conceive  of  a  square  prism 
of  water  (Fig.  80)  in  the  midst  of  a 
body  of  water,  its  upper  surface  coin- 
ciding with  the  free  surface  of  the 
liquid.  Let  the  prism  be  4  cm.  deep 
andl  cm.  square  at  the  end;  then  the 
area  of  one  of  its  ends  is  1  cm.2,  and 
the  volume  of  the  prism  is  4  cc.  "Now 
the  weight  of  4  cc.  of  water  is  4  g.,  and 
hence  this  prism  must  exert  a  down- 
ward pressure  of  4  g.  upon  an  area  of 
1cm.2  But  at  the  same  depth  the 

pressure  in  all  directions  is  the  same ;  hence,  generally,  the 
pressure  at  any  depth  in  water  may  be  taken  approximately 


FIG.  so. 


RULES   FOR    CALCULATING   LIQUID   PRESSURE.      103 

as  one  gram  per  square  centimeter  for  each  centimeter  of 
depth  (=0=  1,000  k.  per  m.2  for  each  meter  of  depth ;  or,  since 
the  weight  of  water  is  about  62.3  pounds  per  cubic  foot,  the 
pressure  is  62.3  pounds  per  square  foot  for  each  foot  of  depth). 
To  determine  the  pressure  at  any  given  depth  in  any  other 
liquid,  the  water  pressure  at  the  given  depth  must  be  multi- 
plied by  the  specific  density  (see  Appendix)  of  the  liquid. 

99.  Rules  for  Calculating  Liquid  Pressure  against  the  Bot- 
tom and  Sides  of  a  Containing  Vessel.    The  total  pressure  due  to 
gravity  on  aMy  portion  of  the  horizontal  bottom  of  a  vessel  contain- 
ing a  liquid  is  equal  to  the  weight  of  a  column  of  the  same  liquid 
whose  base  is  the  area  of  that  portion  of  the  bottom  pressed  upon, 
and  whose  hight  is  the  depth  of  the  water  in  the  vessel. 

Evidently,  the  lateral  pressure  at  any  point  of  the  side  of 
a  vessel  depends  upon  the  depth  of  that  point ;  and,  as  depth 
at  different  points  of  a  side  varies,  to  find  the  total  pressure 
upon  any  portion  of  a  side  of  a  vessel,  find  the  weight  of  a 
column  of  liquid  whose  base  is  the  area  of  that  portion  of  the 
side,  and  whose  hight  is  the  average  depth  of  that  portion. 

100.  The  Surface  of  a  Liquid  at  Rest  is  Level.    By  jolting  a 
vessel,  the  surface  of  a  liquid  in  it  may  be  made  to  assume  the 
form  seen  in  Fig.  81.     Can  it  retain  this 

form  ?     Take  two  molecules  of  the  liquid  at 
the  points  a  and  b,  on  the  same  level.     The 
total  downward  pressures  upon  a  and  b  are 
in  the  ratio  of  their  respective  depths,  c  a 
and  d  b.     But  since  the  pressure  at  a  given 
depth  is  equal  in  all  directions,  c  a  and  d  b 
represent  the  lateral  pressures  at  the  points 
a  and   b,  respectively.     But  d  b  is  greater  than   c  a ;  hence, 
the  molecules   a  and  b,  and  those  lying  in  a  straight  line 
between  them,  are  acted  upon  by  two  unequal  forces  in  op- 
posite directions.     Hence,  the  liquid  cannot  remain  at  rest  in 


104 


MOLAR    DYNAMICS. 


the  position  assumed,  and  there  will,  therefore,  be  a  movement 
of  molecules  in  the  direction  of  the  greater  force,  toward  a, 
till  there  is  equilibrium  of  forces,  which  will  occur  only  when 
the  points  a  and  b  are  equally  distant  from  the  surface ;  or,  in 
other  words,  there  will  be  no  rest  till  all  points  in  the  surface 
are  on  the  same  level. 

This  fact  is  commonly  expressed  thus  :  "  Water  seeks  its  lowest  level." 
In  accordance  with  this  principle,  water  flows  down  an  inclined  plane, 
and  will  not  remain  heaped  up.  An  illustration  of  the  application  of 


FIG.  82. 

this  principle,  on  a  large  scale,  is  found  in  the  method  of  supplying  cities 
with  water.  Fig.  82  represents  a  modern  aqueduct,  through  which  water 
is  conveyed  from  an  elevated  pond  or  river,  a,  beneath  a  river,  b,  over  a 
hill,  c,  through  a  valley,  d,  to  a  reservoir,  e,  from  which  water  is  dis- 
tributed by  service-pipes  to  the  dwellings,  f,  in  a  city. 


EXERCISES. 

1.   The  areas  of  the  bottoms  of  vessels  A,  B,  C,  and  D  (Fig.  83)  are 
equal.     The  vessels  have  the  same  depth,  and  are  filled  with  water,     (a) 

Which  vessel  contains  the 
most  water  ?  (6)  On  the 
bottom  of  which  vessel  is 
the  pressure  equal  to  the 
weight  of  the  water  which 

it  contains  ?       (c)    How 
c  u 

does  the  pressure  upon 

the  bottoms  of  vessels  A, 
B,  and  C  compare  with  the  weight  of  the  water  in  them,  respectively  ? 


EXERCISES.  105 

2.  A  cubic  foot  of  water  weighs  about  62.3  pounds.     Suppose  that 
the  area  of  the  bottom  of  each  vessel  is  100  square  inches,  and  the  depth 
is  14  inches,  what  is  the  pressure  on  the  bottom  of  each  ? 

3.  The  bottom  of  vessel  A  is  square.   What  is  the  total  pressure  against 
one  of  its  vertical  sides  ? 

4.  Let  A  (Fig.  84)  be  a  cubical  tank  whose  inside  dimension  is  20  inches. 
Leading  from  its  side  is  a  tube  whose  top  is  80  inches  above  the 

interior  top  surface  of  the  tank,  (a)  What  mass  of  water  will 
the  tank  (not  including  the  tube)  contain  ?  (6)  Suppose  the 
tank  and  tube  to  be  filled  with  water,  what  pressure  will  be 
exerted  upon  the  bottom  of  the  tank  ?  (c)  What  upon  the 
top  of  the  tank  ?  (d)  What  upon  one  of  its  sides  ? 

5.  Suppose  that  the  area  of  the  end  of  the  large  piston  of 
of  a  hydrostatic  press  is  100  square  inches,  what  must  be  the 
area  of  the  end  of  the  small  piston  that  a  force  of  100  pounds 
applied  to  it  may  produce  a  pressure  of  2  tons  ? 


A 


C 


6.  Take  a  glass  U-tube  (Fig.  85)  about  40  inches  high,  having 
a  stout  rubber  tube,  a,  attached,  and  containing  mercury  with 
the  surfaces  at  the  same  level  in  both  arms.     Blow  into  the      FIQt  34. 
tube ;  the  surfaces  of  mercury  will  at  once  assume  different 
levels.     How  will  you  determine  the  pressure  which  you  exert  through 
the  air  in  the  tube  upon  the  mercury  (the  specific  density  of  mercury  being 
13.59)? 

7.  (a)  Suck  air  from  a.    What  happens  to  the  mercury  ?    (6)  How  may 
you  determine  the  diminution  of  pressure  which  you  produce  by  suction  ? 

8.  Take  a  similar  tube  containing  water  instead  of  mercury,  connect 
it  with  a  gas  jet  and  turn  on  the  gas.     How  would  you  determine  how 

much  greater  (or  less)  its  pressure  is  than  that  of  the 
atmosphere  ? 

9.    How  great  is  the  hydrostatic  pressure  in  fresh 
water  at  the  depth  50  feet  ? 

10.    (a)  A  "house  is  supplied  with  water  by  a  system 
of  pipes  from  a  distant  reservoir,  as  is  customary  in 
cities.    What  data  should  you  require  in  order  to  com- 
pute the  pressure  at  any  point  in  the  pipe  ?     (b)  How 
FIG  85.  much  greater  is  the  pressure  at  a  point  in  the  pipe  in 

the  cellar  than  at  another  point  in  the  attic  ?  (c)  Is 
the  pressure  in  the  pipe  the  same  when  water  is  running  from  a  faucet  in 
the  house  as  when  the  water  is  at  rest  ? 

11.  Suppose  that  the  aqueduct  at  point  b  (Fig.  82)  is  150  feet  below  the 
level  of  the  pond,  what  is  the  pressure  at  this  point  (expressed  in  tons 
per  square  foot)  tending  to  burst  the  walls  of  the  aqueduct  ? 


106 


MOLAR    DYNAMICS. 


SECTION     II. 

ATMOSPHERIC    PRESSURE. 

101.  Introduction.  We  live  at  the  bottom  of  an  exceed- 
ingly rare  and  elastic  ocean  of  air,  called  the  atmosphere. 
Every  molecule  in  this  gaseous  ocean  is  drawn  towards  the 
earth's  center  by  gravitation,  and  the  atmosphere  is  thus 


FIG.  86. 


bound  to  the  earth  by  this  force,  just  as  is  the  liquid  ocean. 
Evidently  the  pressure  in  the  atmosphere  due  to  its  weight 
increases  with  the  depth;  or,  since  in  our  position  we  are 
more  accustomed  to  speak  of  hight  in  the  atmosphere,  de- 
creases with  the  hight.  The  pressure  does  not  diminish 
regularly  with  the  hight  as  in  an  ocean  of  incompressible 


ATMOSPHERIC    PRESSURE. 


107 


FIG.  87. 


fluid.     Air    is    very   compressible;    the   lower  strata  of   the 

atmosphere,  which  sustain  the  weight  of  the  upper  strata,  are 

much  compressed,  and  are  therefore  relatively  very  dense. 

The  density  of  the  air  diminishes  more  rapidly  than  the  hight 

above  sea  level  increases.     Owing  to 

this  fact,  the  greater  part  of  the  mass 

of  the  atmosphere  is  within  three  and 

a  half  miles  of  the  sea  level.     Above 

this  hight  the  air  is  much  rarified  and 

vanishes,  as  it  were,  very  gradually 

into  airless  space.1 

Experiment  1.    Fill  (or  partly  fill)  a 

tumbler  with  water,  cover  the  top  closely 

with  a  card    or   writing-paper,   hold    the 

paper  in  place  with  the  palm  of  the  hand, 

and  quickly  invert  the  tumbler  (Fig.  87). 

How  is  the  water  supported  ? 

Experiment  2.  Force  the  piston  A 
(Fig.  88)  of  the  seven-in-one  apparatus 
quite  to  the  closed  end  of  the  hollow 
cylinder,  and  close  the  stop-cock  B.  Try 
to  pull  the  piston  out  again.  Why  do 
you  not  succeed  ?  Hold  the  apparatus 
in  various  positions,  so  that  the  atmos- 
phere may  press  down,  laterally,  and 

up,  against  the  piston.     You  discover  no  difference  in  the  pressure  which 

it  receives  from  different  directions. 

Atmospheric  pressure  is  exerted  all  over  the  outside  of  a  body,  so  that 

usually  it  is  not  noticeable.     But  if,  as  in  the  case  of  the  piston,  pressure 

be  removed  from  one  side  of  a  body,  the  other  side  experiences  the  whole 

unbalanced  pressure. 

1  The  shading  in  Fig.  86  is  intended  to  indicate  roughly  the  variation  in  the 
density  of  the  air  at  different  elevations  ahove  sea  level.  The  figures  in  the  left 
margin  show  the  hight  in  miles ;  those  in  the  first  column  on  the  right,  the  corre- 
sponding average  hight  of  the  mercurial  column  in  inches  ;  and  those  in  the  extreme 
right,  the  density  of  the  air  compared  with  its  density  at  sea  level.  If  the  aerial 
ocean  were  of  a  density  equal  to  that  at  sea  level,  its  hight  would  be  a  little  less  than 
5  miles.  Only  the  highest  peaks  of  the  Himalaya  Mountains  would  rise  above  it. 
If  an  opening  were  made  in  the  earth  35  miles  in  depth  below  sea  level,  the  density 
of  the  air  at  the  bottom  would  be  greater  than  that  of  water. 


FIG.  88. 


108  MOLAR   DYNAMICS. 

102.  How  Atmospheric  Pressure  is  Measured. 

Experiment  3  (preliminary).     Take  a  U-shaped  glass  tube  (Fig.  89), 

half  fill  it  with  water,  close  one 
end  with  a  thumb,  and  tilt  the 
tube  so  that  the  water  will  run 
into  the  closed  arm  and  fill  it ; 
then  restore  it  to  its  original  ver- 
tical position.  Why  does  not  the 
water  settle  to  the  same  level  in 
FIG.  89.  both  arms  ? 

Let  Fig.  90  represent  a  U-shaped  glass  tube  closed  at  one 
end,  about  34  inches  in  hight,  and  having  a  bore  of  1  square- 
inch  section.     The  closed  arm  having  been  rilled 
with  mercury,  the  tube  is  placed  with  its  open 
end  upward,  as  in  the  cut.     The  mercury  in  the 
closed  arm  sinks  about  2  inches  to  A  and  rises  2 
inches  in  the  open  arm  to  C ;  but  the  surface  A  is 
30  inches  higher  than  the  surface  C.     This  can 

ji|     ^ 

be  accounted  for  only  by  the  atmospheric  pres- 
sure. The  column  of  mercury  B  A,  containing  30 
cubic  inches,  is  an  exact  counterpoise  for  a  column 
of  air  of  the  same  diameter  extending  from  C  to 

the  upper  limit  of  the  atmospheric  ocean,  —  an 

i  i-ij_  FIG.  90. 

unknown  hight. 

The  weight  of  the  30  cubic  inches  of  mercury  in  the  column 
B  A  is  14.7  pounds.  Hence  the  weight  of  a  column  of  air  of 
1  square-inch  section,  "extending  from  the  surface  of  the  sea  to 
the  upper  limit  of  the  atmosphere,  is  about  14.7  pounds.  But 
in  fluids  gravitation  causes  equal  pressure  in  all  directions. 
Hence,  at  the  level  of  the  sea,  all  bodies  are  pressed  upon  in  all 
directions  by  the  atmosphere  with  a  force  of  about  14.7  pounds 
per  square  inch,  or  about  one  ton  per  square  foot. 

103.  Standard  Pressure.    Many  physical  operations  require 
a  standard  pressure  for  reference.     The  standard  generally 


THE    BAROMETER. 


109 


adopted  is  the  pressure  exerted  by  a  column  of  pure  mercury 
at  0°  C.  and  76  cm.  (29.922  inches)  high,  which  is  about  the 
average  hight  of  the  barometric  column  at  sea  level  in  latitude 
45°.  The  pressure  corresponding  to  this  hight  is  1033.3  grams 
per  square  centimeter,  or  14.7  pounds  per  square  inch. 

A  pressure  of  14.7  pounds  per  square  inch  is  quite  generally 
adopted  by  engineers  as  a  unit  of  pressure,  and  is  called  an 
atmosphere.  Physicists,  however,  generally  measure  gaseous 
pressure  in  terms  of  mm.  of  mercury  at  0°  C. ;  that  is,  the 
hight  in  mm.  of  mercury  that  the 
given  pressure  would  sustain  in 
the  vacuum  tube. 

104,    The  Barometer,      The 

hight  of  the  column  of  mercury 
supported  by  atmospheric  pres- 
sure is  quite  independent  of  the 
area  of  the  surface  of  the  mer- 
cury pressed  upon ;  hence,  the 
apparatus  is  more  conveniently 
constructed  in  the  form  repre- 
sented in  Fig.  91. 

A  straight  tube  about  34 
inches  long  is  closed  at  one  end 
and  filled  with  mercury.  The 
tube  is  inverted,  with  its  open 
end  tightly  covered  with  a  finger,  and  this  end  is  inserted  into 
a  vessel  of  mercury.  When  the  finger  is  withdrawn,  the  mer- 
cury sinks  until  there  is  equilibrium  between  the  downward 
pressure  of  the  mercurial  column  A  B  and  the  pressure  of  the 
atmosphere.  The  empty  space  at  the  top  of  the  tube  is  called 
a  Torricellian l  vacuum.  An  apparatus  designed  to  measure 
atmospheric  pressure  is  called  a  barometer  (pressure-measurer). 


FIG.  91. 


1  Tlie  first  barometer  was  constructed  by  Torricelli,  a  Florentine,  in  1613. 


110  MOLAB,   DYNAMICS. 

A  common  and  inexpensive  form  of  barometer  is  represented 
in  Fig.  92.  Beside  the  tube  and  near  its  top  is  a  scale, 
graduated  in  inches  or  centimeters,  indicating  the  hight  of 
the  mercurial  column.  For  ordinary  purposes  this 
scale  needs  to  have  a  range  of  only  three  or  four 
inches,  so  as  to  include  the  maximum  fluctuations  of 
the  column.1 

Fluctuations  in  barometric  pressure  are  of  hourly 
occurrence.  Some  of  the  many  conditions  which  in- 
fluence atmospheric  pressure  are  changes  in  tempera- 
ture, humidity  of  the  air,  and  currents  in  the  atmospheric 
ocean.2 


105.  The  Fortin  Barometer.  We  will  suppose  the  scale 
of  a  barometer  to  be  fixed  so  as  to  indicate  correctly  the  hight 
of  the  surface  of  mercury  in  the  tube  above  that  in  the  cistern 
at  a  time,  for  instance,  when  this  distance  is  30  inches.  A  point 
on  the  surface  of  the  mercury  in  the  cistern  in  this  case  is  called 
technically  the  zero  point.  Now,  should  the  mercury  in  the  tube 
fall  to  29  and  the  mercury  in  the  cistern  remain  at  zero,  then 
the  scale  reading  would  indicate  correctly  the  barometric  hight. 
Cut  the  mercury  does  not  remain  at  zero,  but  rises  a  little  (less 
as  the  diameter  of  the  cistern  is  greater) ;  consequently,  the  scale 
G'  92'  reading  is  too  great.  When  the  mercury  in  the  tube  is  higher 
than  30  all  the  readings  will  be  too  small.  Evidently,  then,  the  mercury 
in  the  cistern  must  be  brought  to  zero  at  every  observation  in  order  to 
eliminate  this  error.  This  is  easily  accomplished  in  the  Fortin  barometer. 
The  bottom  of  the  cistern  of  this  barometer  is  of  pliable  leather,  resting  on 


1  At  the  Central  Station  in  Boston,  Feb.  8,  1895,  the  mercury  fell  to  28.61  in.,  the 
lowest  on  record  at  this  station.    The  highest  point  ever  recorded  at  this  station  was 
30.97  in.,  on  Dec.  1,1887. 

"  A  variation  of  two  inches  in  barometric  hight  is  attended  by  a  corresponding 
variation  in  the  hight  of  tides  at  the  place  of  about  three  feet."  —  G.  H.  DARWIN. 

2  The  barometer  is  sometimes  called  a  "  weather-glass,"  chiefly  because  its  scale 
frequently  bears  the  words  fair,  rainy,  storm,  etc.    These  words  are  very  objection- 
able, since  they  are  totally  misleading  from  a  meteorological  point  of  view.    To  form 
a  forecast  of  the  weather  of  much  value,  a  barometer,  a  thermometer,  and  a  hygrom- 
eter must  be  consulted,  and  one  must  be  familiar  with  the  laws  which  govern  the 
relations  between  atmospheric  pressure,  temperature,  moisture,  etc. 


BAROMETRIC    MEASUREMENT    OF    HIGHTS. 


Ill 


a  thumb-screw,  A  (Fig.  93).  Projecting  from  the  tube  inside  of  the  cistern 
is  a  little  pointer,  B,  of  colored  glass.  The  lower  end  of  this  pointer, 
called  the  fiducial  point,  corresponds  to  the  zero  point. 
The  level  of  the  mercury  in  the  cistern  must  be  set  to 
this  point  by  raising  or  lowering  the  cistern  base  by  the 
adjusting  screw,  before  taking  a  reading.  A  sliding  piece, 
C  (Fig.  94),  furnished  with  a  vernier,  can  be  slid  along 
the  tube  so  as  to  enable  one  to  read  with  great  accuracy. 
In  refined  scientific  researches  it  is  necessary  to  make 
suitable  allowances  for  expansion  and  contraction  of  the 
mercury  attending  changes  in  temperature,  hence  a  very 
sensitive  thermometer  is  attached  to  the  barometer. 


-J) 


il 


FIG.  93, 


106.  Barometric  Measurement  of 
Hights,  Since  atmospheric  pressure 
varies  with  the  hight  above  sea  level, 
it  is  evident  that  changes  in  elevation 
may  be  determined  from  changes  of 
pressure  as  indicated  by  the  barometer. 
For  example,  the  hight  of  a  mountain 
may  be  ascertained  from  barometric 
readings  made  at  the  same  time  on  the 
summit  and  at  sea  level.  For  moderate 
hights  the  barometric  column  falls  at 


FIG.  94. 

a  nearly  uniform  rate  of  one  inch   for  every  900  feet  of 
ascent. 

EXERCISES. 

1.  The   average  barometric  hight  in  the  city  of  Denver  is  24.5  in. 
What  is  the  average  atmospheric   pressure  in  this  city,  expressed  in 
pounds  per  square  inch  ? 

2.  When  the  barometric  column  stands  at  748  mm.,  what  is  the  atmos- 
pheric pressure,  expressed  in  grams  per  cm.2  ? 

3.  What  is  the  hight  of  the  barometric  column  when  the  pressure  of 
the  air  is  1045  g.  per  cm.2  ? 

4.  Suppose  that,  on  a  day  when  the  pressure  of  the  air  is  756  mm.,  air 
is  exhausted  from  the  receiver  of  an  air-pump  until  the  mercury  in  a 
barometer  placed  in  the  receiver  stands  at  30  mm. ,  what  per  cent  of  the 
air  has  been  removed. 


112 


MOLAR    DYNAMICS. 


SECTION   III. 

RELATION  BETWEEN  THE  DENSITY,  VOLUME,  AND 
PRESSURE  OF  A  BODY  OF  GAS. 

107.  Elasticity  of  Gases,  The  elasticity  of  all  fluids  is 
perfect.  By  this  is  meant  that  the  force  exerted  in  expan- 
sion is  equal  to  the  force  used  in  compression  ; 
and  that,  however  much  a  fluid  is  compressed, 
it  will  always  completely  regain  its  former  vol- 
ume when  the  pressure  is  removed.  Hence  the 
barometer,  which  measures  the  compressing  force 
of  the  atmosphere,  also  measures  at  the  same 
time  the  elastic  force  of  the  air.  A  so-called 
vacuum  gauge  (Fig.  95)  is  simply  a  short  mer- 
cury barometer,  —  short  because  it  is  seldom 

required  to  make  measurements  except  in  toler- 
ably high  vacua,  where  the  mercurial  column 
is  correspondingly  low.  For  instance,  this 
apparatus,  placed  under  the  receiver  of  an  air- 
pump  from  which  air  is  exhausted,  will  measure 
the  elastic  force  of  the  air  in  the  receiver.  This 
__32  known,  the  degree  of  exhaustion  is  readily 
determined. 


FIG.  95. 


-.-Bi 


108.    Boyle's  (or  Mariotte's)  Law. 

Experiment.     Take  a  bent  glass  tube  (Fig.  96),  the 


short  arm  being  closed,  and  the  long  arm,  which  should 
be  at  least  34  inches  (85  cm.)  long,  being  open  at  the  top. 
Pour  mercury  into  the  tube  till  the  surfaces  in  the  two 
arms  are  at  the  same  level  A  B.  The  body  of  air  to  be 
experimented  with  is  in  the  short  arm  between  A  and  C. 
The  dimensions  of  this  body  can  vary  only  in  hight  ; 
hence  its  hight,  7J,  may  represent  its  volume.  Measure 
H  (i.e.  the  distance  between  A  and  C)  and  regard  the  number  of  inches 
(or  centimeters)  as  representing  the  volume,  V.  Its  pressure,  P,  evidently 


FiQ.  96. 


EXERCISES.  113 

is  the  same  as  that  of  the  atmosphere  at  the  time.  Consult  a  barometer, 
and  ascertain  the  hight  of  the  barometric  column  ;  represent  this  hight 
by  P.  Pour  a  little  mercury  into  the  tube  ;  the  mercury  rises  (say)  to  AI 
and  BI.  Measure  the  vertical  distance  between  AI  and  C  ;  this  number 
represents  the  volume,  FI,  of  the  body  of  air  now.  Measure  the  vertical 
distance  between  AI  and  BI  ;  this  number  represents  the  increase  in 
pressure,  which,  added  to  P,  gives  its  present  pressure,  PI. 

Now  pour  more  mercury  into  the  tube,  so  that  it  will  rise  to  (say) 
A2  and  B2.  Determine  as  before  the  new  volume,  F2,  and  the  new  pres- 
sure, P2.  So  continue  to  add  mercury  a  third  and  a  fourth  time,  and 
get  new  values  for  the  volume,  F3  and  F4,  and  for  the  pressure,  P3  and 
P±.  Arrange  the  results  as  follows : 

F  ==....  P- F  x  P  = 

Fi=....  P!= FiXP1  = 

F2  = P2  = F2  X  P2  = 

etc.  etc. 

It  will  be  found  that  the  series  of  products  in  the  last  column  are 
approximately  equal  (due  allowance  being  made  for  errors  in  measure- 
ment, etc.)  ;  consequently,  the  product  of  the  volume  of  a  body  of  gas 
multiplied  by  its  pressure  is  constant,  and  the  volume  varies  inversely  as 
its  pressure.  Hence  the  (Boyle's)  law  : 

The  volume  of  a  body  of  gas  at  a  constant  temperature  varies  inversely 
as  its  pressure,  density,  and  elasticity.^ 

EXERCISES. 

1.  If  the  volume  of  a  certain  body  of  gas  be  500  cc.  when  its  pressure 
is  800  g.  per  cm.2,  what  is  the  volume  of  the  same  body  when  its  pressure 
is  1200  g.  per  cm.2. 

2.  If  a  body  of  air  whose  volume  is  1m.3  and  pressure  is  760  mm. 
expands  and  occupies  4.5  m.3,  what  will  be  its  pressure  ? 

3.  A  bubble  of  air  liberated  at  a  depth  of  2  meters  in  water  has  a 
volume  of  3  cm.3.     What  will  be  its  volume  when  it  has  risen  1  meter  ? 

1  For  many  years  after  the  announcement  of  this  law  it  was  believed  to  be  rigor- 
ously correct  for  all  gases  ;  but  more  recently  more  precise  experiments  have  shown 
that  it  is  approximately  but  not  rigidly  true  for  any  gas.  There  is  a  limit  beyond 
which  this  law  does  not  hold.  This  limit  is  soonest  reached  with  those  gases,  like 
carbon-dioxide,  chlorine,  etc.,  that  are  most  readily  liquefied.  A  gas  conforms  more 
nearly  to  Boyle's  law,  in  proportion  as  it  is  farther,  as  regards  both  pressure  and 
temperature,  from  its  liquefying  point.  As  a  gas  approaches  this  point  its  density 
increases  more  rapidly  than  its  elasticity. 


114 


MOLAR    DYNAMICS. 


4.  Air  is  rarefied  in  the  receiver  of  an  air-pump  so  that  the  difference 
in  level  of  the  two  surfaces  of  mercury  in  the  vacuum  gauge  is  .2  mm. 
What  is  the  elastic  force  of  the  remaining  air,  expressed  in  grams  per  cm.2  ? 

5.  A  mass  of  air  occupies  80  cc.  when  the  pressure  is  100  mm.    What 
space  will  it  occupy  when  the  pressure  is  150  mm.? 

6.  A  mass  of  air  occupies  160  cc.  when  the  pressure  is  760  mm.    What 
must  be  the  pressure  that  it  shall  occupy  only  50  cc.  ? 


SECTION   IV. 


PUMPS   AND   SIPHONS. 


109.   The  Air-pump. 


FIG.  97. 


The  air-pump  is  used  to  rarefy  air  in  a  closed 
J..J  vessel.  Fig.  97  will  illus- 
trate its  operation.  R 
is  a  glass  receiver  within 
which  the  air  is  to  be 
rarefied  ;  B  is  a  hollow 
cylinder  of  brass,  called 
the  pump-barrel;  the 
plug  P,  called  a  piston, 
is  fitted  to  the  interior 
of  the  barrel,  and  can 
be  moved  up  and  down 
by  the  handle  H  ;  s  and 
t  are  valves.  A  valve 
acts  on  the  principle  of 
a  door  intended  to  open 


or  close  a  passage.  If  you  walk  against  a  door  on  one  side,  it  opens  and 
allows  you  to  pass  ;  but  if  you  walk  against  it  on  the  other  side,  it  closes 
the  passage  and  stops  your  progress. 

Suppose  the  piston  to  be  in  the  act  of  descending ;  the  compression  of 
the  air  in  B  closes  the  valve  t,  and  opens  the  valve  s,  and  the  enclosed 
air  escapes.  After  the  piston  reaches  the  bottom  of  the  barrel,  it  begins 
its  ascent.  This  would  cause  a  vacuum  between  the  bottom  of  the  barrel 
and  the  ascending  piston  (since  the  unbalanced  pressure  of  the  outside  air 
immediately  closes  the  valve  s),  but  the  pressure  of  the  air  in  the  receiver 
R  opens  the  valve  t  and  fills  this  space.  As  the  air  in  R  expands,  it 
becomes  rarefied  and  exerts  less  pressure.  The  external  pressure  of  the 
air  on  R,  being  no  longer  balanced  by  the  pressure  of  the  air  within, 
presses  the  receiver  firmly  upon  the  plate  L.  Each  repetition  of  a  double 


LIFTING-PUMP    FOR    LIQUIDS. 


115 


stroke  of  the  piston  results  in  the  removal  of  a  portion  of  the  air  remain- 
ing in  R.     The  air  is  removed  from  R  by  its  own  expansion. 

However  far  the  process  of  exhaustion  may  be  carried,  the  receiver  will 
always  be  filled  with  air,  although  it  may  be  exceedingly  rarefied.  The 
operation  of  exhaustion  is  practically  ended  when  the  pressure  of  the  air 
in  R  becomes  too  feeble  to  lift  the  valve  t,  unless  the  apparatus  be  so 
constructed  that  the  valves  are  opened  and  closed  by  mechanical  action. 
It  is  obvious  that  if  s  and  t  opened  downward  instead  of  upward,  then  as 


FIG.  99. 


FIG.  100. 


the  piston  was  raised  and  depressed,  air  would  be 
compressed  in  R.  A  condenser  is  merely  a  pump 
with  its  valves  reversed,  and  is  used  to  condense 
air. 

In  recent  years  the  so-called  mercury  air-pump 
has  largely  displaced  the  pump  described  above, 
since  it  is  capable  of  producing  a  much  greater 
rarefaction.     In  brief,  it  makes  use  of  the  Torri- 
cellian vacuum,  such  as  is  formed  in  the  top  of  a  barometer  tube. 


FIG, 


110.  Lifting-pump  for  Liquids.  The  common  lifting-pump  is 
constructed  like  the  barrel  of  an  air-pump.  Fig.  98  represents  the  piston 
B  in  the  act  of  rising.  As  the  air  is  rarefied  below  it,  water  rises  in 
consequence  of  atmospheric  pressure  on  the  water  in  the  well,  and  opens 
the  lower  valve  D.  Atmospheric  pressure  closes  the  upper  valve  C  in 
the  piston.  When  the  piston  is  pressed  down  (Fig.  99),  the  lower  valve 
closes,  the  upper  valve  opens,  and  the  water  between  the  bottom  of  the 
barrel  and  the  piston  passes  through  the  upper  valve  above  the  piston. 


116 


MOLAR    DYNAMICS. 


When  the  piston  is  raised  again  (Fig.  100),  the  water  above  the  piston  is 
raised  and  discharged  from  the  spout. 

111.     Force-pump.     In  this  pump  the  ordinary  piston  with  valve  is 
replaced  by  a  solid  cylinder  of  metal,  B  (Fig.  101),  called  the  plunger. 

This  passes  through  a  stuffing  box,  D,  in 
which  it  fits  air-tight.  Valves  opening 
upward  and  outward  are  placed  at  A  and 
C,  respectively.  When  the  plunger  is 
raised,  A  opens  and  C  closes,  and  water 
is  raised  into  the  barrel  by  atmospheric 
pressure.  When  the  plunger  descends,  A 
closes  and  C  opens,  and  the  water  is  forced 
up  through  the  pipe  E.  An  air-dome,  F, 
is  usually  connected  with  these  pumps  to 
regulate  the  pressure  so  as  to  give  through 
the  delivery  pipe  a  very  steady  stream. 
This  dome  contains  air.  When  the 
plunger  descends  it  forces  water  into  the 
dome  and  compresses  the  air  within.  As 
soon  as  the  down  stroke  of  the  piston 
ceases,  the  valve  C  closes,  and  the  com- 
pressed air  in  the  dome  forces  the  water 


FIG.  101. 


out  through  E  in  a  continuous  stream. 

112.  Siphon.  Take  two  vessels,  A  and  B  (Fig.  102),  con- 
taining water  (or  other  liquid).  Let  the  surface  of  the  liquid 
in  one  vessel  be  lower  than  the  sur-  _ 

face  in  the  other.  Bend  a  tube,  C  C, 
of  any  kind  (e.g.  rubber  or  glass) 
into  the  form  of  the  letter  U,  fill  it 
with  some  of  the  same  liquid,  cover 
the  ends  with  your  fingers,  invert 
the  tube,  dip  the  ends  of  the  tube 
into  the  liquids  and  remove  the  fin- 
gers. Liquid  will  flow  from  the 
vessel  in  which  the  liquid  has  a 
higher  level  into  the  other  vessel.  How  does  the  atmospheric 
pressure  upon  the  surfaces  of  the  liquids  in  the  two  vessels 


F 


FIG.  102. 


THE    PRINCIPLE    OF    ARCHIMEDES.  117 

compare  ?  The  flow  of  liquid  shows  the  existence  of  an 
unbalanced  force.  How  do  you  account  for  the  unbalanced 
force  ?  How  great  is  this  unbalanced  force  ?  As  the  liquids 
in  the  two  vessels  approach  the  same  level,  does  this  unbal- 
anced force  change  in  magnitude  ?  What  will  happen  when 
the  liquids  in  the  two  vessels  reach  the  same  level  ?  If 
vessel  B  were  removed,  would  the  liquid  flow  from  vessel  A  ? 
A  tube  used  in  this  manner  for  transferring  a  liquid  through 
the  agency  of  atmospheric  pressure  is  called  a  siphon. 

SECTION  V. 
THE   BUOYANT   FORCE   OF   FLUIDS. 

113,  The  Principle  of  Archimedes.  Suppose  d  c  b  a  (Fig. 
103)  to  be  a  cubical  block  of  marble  immersed  in  a  liquid. 
It  is  obvious  that  the  difference  between  the  upward  pressure 
against  the  surface  c  b  and  the  downward 
pressure  on  the  surface  d  a  is  the  weight  of 
a  column  of  liquid,  e  c  b  o,  less  the  weight  of  a 
column  of  liquid,  e  d  a  o,  which  is  a  column  of 
liquid,  dcba(ecbo  —  edao^dcba).  But 
a  column  of  liquid,  d  c  b  a,  has  precisely  the 
volume  of  the  solid  submerged.  Therefore, 
a  body  is  buoyed  up  by  a  fluid  in  consequence 


of  the  unequal  pressures  upon  its  top  and  bot-  pIG  10s. 

torn  at  their  different  depths,  and  the  amount 
of  the  buoyancy  is  the  weight  of  a  volume  of  that  fluid  equal  to 
the  volume  of  the  immersed  body. 

This  principle,  commonly  called  the  Principle  of  Archimedes, 
from  the  name  of  the  discoverer,  may  be  thus  stated  :  a  body 
immersed  in  a  fluid  is  buoyed  up  by  a  force  equal  to  the  weight 
of  the  fluid  displaced. 

Experiment  1.  Suspend  from  one  arm  of  a  balance  beam  a  cylin- 
drical bucket,  A  (Fig.  104),  and  from  the  bucket  a  solid  cylinder,  B,  whose 
volume  is  exactly  equal  to  the  capacity  of  the  bucket ;  in  other  words, 


118 


MOLAR    DYNAMICS. 


the  latter  would  just  fill  the  former.      Counterpoise  the   bucket   and 

cylinder  with  weights. 

Place  beneath  the  cylinder  a  tumbler  of  water,  and  raise  the  tumbler 
until  the  cylinder  is  completely  submerged. 
The  buoyant  force  of  the  water  destroys  the 
equilibrium.  Pour  water  into  the  bucket. 
When  it  becomes  just  even  full,  the  equilib- 
rium is  restored. 

Now  it  is  evident  that  the  cylinder 
immersed  in  the  water  displaces  its  own 
volume  of  water,  or  just  as  much  water 
as  fills  the  bucket.  But  the  bucket  full  of 
water  is  just  sufficient  to  restore  the  weight 
lost  by  the  submersion  of  the  cylinder. 
What  principle  does  this  experiment  illus- 
illllilllli  trate? 


FIG. 104. 


A  floating  body  (as  a  cork  011  water) 
sinks  until  it  displaces  a  mass  of  the 
fluid  equal  to  its  own  mass,  or  until  it  reaches  a  depth  ivhere 
the  upward  pressure  of  the  fluid  is  equal  to  its  own  weight. 

Experiment  2.  Place  a  baroscope  (Fig.  105),  consisting  of  a  scale- 
beam,  a  small  weight,  and  a  hollow  brass  sphere,  under  the  receiver  of  an 
air-pump,  and  exhaust  the  air.  In  the  air  the 
weight  and  sphere  balance  each  other ;  but  when 
the  air  is  removed,  the  sphere  sinks,  showing  that 
in  reality  it  is  heavier  than  the  weight.  In  the  air 
each  is  buoyed  up  by  the  weight  of  the  air  it  dis- 
places ;  but  as  the  sphere  displaces  more  air,  it  is 
buoyed  up  more.  Consequently,  when  the  buoyant 
force  is  withdrawn  from  both,  their  equilibrium  is 
destroyed. 

The  absolute  weight  of  a  body  is  its  weight 
in  a  vacuum.     How  much  greater  is  this 

weight  than  the  weight  of  the  body  in  air  ? 

FIG. 105. 

The  density  of  the  atmosphere  is  greatest  at  the  surface  of  the  earth. 
A  body  free  to  move  cannot  displace  more  than  its  own  weight  of  a 
fluid  ;  therefore  a  balloon,  which  is  a  large  bag  filled  with  a  gas  many 


ARCHIMEDES. 

[From  bust  in  National  Museum,  Naples.] 


SPECIFIC    DENSITY    AND    SPECIFIC    GRAVITY.        119 

times  lighter  than  air  at  the  sea  level,  will  rise  till  the  weight  of  the 
balloon,  together  with  its  car  and  cargo,  equals  the  weight  of  the  air 
displaced. 

SECTION   VI. 
DENSITY,    SPECIFIC    DENSITY,    AND     SPECIFIC    GRAVITY. 

114.  Terms  Defined.     The  density  of  a  substance  at  any 
temperature  is  the  mass  per  unit  of  volume  of  the  substance 
at  that  temperature.     Thus,  the    density  of   water   at  4°  C. 
is  one  gram  per  cubic  centimeter,  and   the  density  of   cast 
iron  at  the  same  temperature  is  about  7.12  grams  per  cubic 
centimeter.     The  mean  density  of  a  body  is  found  by  divid- 
ing its  mass  by  its  volume. 

The  specific  density  of  a  substance  is  the  number  which 
expresses  how  many  times  denser  the  substance  is  than  some 
standard  substance.  The  specific  gravity  of  a  substance  is 
the  ratio  of  the  weight  of  a  body  of  that  substance  to  the  weight 
of  an  equal  volume  of  some  standard.  .  The  standard  adopted 
for  solids  and  liquids  is  distilled  water  at  some  definite 
temperature  (in  scientific  work  at  4°  C.).  Evidently  the 
number  which  expresses  the  specific  density  of  a  substance 
and  the  number  which  expresses  the  specific  gravity  of  the 
same  substance  are  identical,  and  both  are  abstract  numbers. 

115.  Formulas  for  Specific  Density  and  Specific  Gravity. 

Let  D  represent  the  density  of  any  given  substance,  and  D' 
the  density  of  water,  and  let  JFand  IF'  represent,  respectively, 
the  weights  of  equal  volumes  of  the  same  substances  ;  then, 
by  definition, 


Density  of  given  substance     D 

~         Density  of  water  =»•=  Sp' 


°T 


„     Weight  of  a  given  volume  of  the  substance  _W_  _  „     ~ 
Weight  of  equal  volume  of  water  W 


120 


MOLA'B  DYNAMICS. 


116.  Experimental  Methods  of  Finding  the  Specific  Grav- 
ity of  Substances.  (1)  Solids.  The  Principle  of  Archimedes 
is  commonly  made  use  of  in  determining  the  specific  gravity 
of  solids. 


Experiment  1.  From  a  hook  beneath  a  scale-pan  (Fig.  106)  suspend 
by  a  fine  thread  a  small  portion  of  the  solid  substance  whose  specific 
gravity  is  to  be  found,  and  weigh  it,  while 
dry,  in  the  air.  Then  immerse  the  body  in 
a  tumbler  of  water  (see  that  it  is  completely 
submerged),  and  weigh  it  in  water.  The  loss 
of  weight  in  water  is  evidently  W,  i.e.  the 
weight  of  the  water  displaced  by  the  body ; 
or,  in  other  words,  the  weight  of  a  body  of 
water  having  the  same  volume  as  that  of  the 
specimen.  Apply  the  formula  (2)  for  finding 
the  specific  gravity. 

Experiment  2.  Take  a  piece  of  sheet 
lead  1  inch  long  and  £  inch  wide,  weigh  it 
in  air  and  then  in  water,  and  find  its  loss 
of  weight  in  water.  Weigh  in  air  a  piece 

of  cork  or  other  substance  that  floats  in  water;   then  fold  the  lead- 
sinker,  place  it  astride  the  string  just  above  the  specimen,  completely 
immerse  both,  and  find  their  combined  weight  in  water.     Subtract  their 
combined  weight  in  water  from  the  sum  of 
their  weights  in  air ;  this  gives  the  weight 
of  water  displaced  by  both.      Subtract 
from  this  the  weight  lost  by  the  lead  alone, 
and  the  remainder  is  W,  i.e.  the  weight 
of  water  displaced  by  the  cork.     Apply 
formula  (2),  as  before. 

(2)  Liquids. 


FIG.  10G. 


FIG.  107. 


Experiment  3.  Take  a  bottle  that 
holds  when  filled  a  certain  (whole)  num- 
ber of  grams  of  water,  e.g.  100  g.,  200  g., 
etc.  Fill  the  bottle  with  the  liquid  whose  specific  gravity  is  sought. 
Place  it  on  a  scale-pan  (Fig.  107),  and  on  the  other  scale-pan  place  a 
piece  of  metal,  a,  which  is  an  exact  counterpoise  for  the  bottle  when 


THE    DENSIMETER. 


121 


empty.  On  the  same  pan  place  weights  b  until  there  is  equilibrium. 
The  weights  placed  in  this  pan  represent  the  weight  W  of  the  liquid  in 
the  bottle.  The  W  (i.e.  the  100  g.,  200  g.,  etc.)  is  usually  etched 
on  bottles  constructed  for  this  purpose.  Apply  formula  (2). 

117.  The  Densimeter.  The  principle  of  the  densi- 
meter (commonly  called  hydrometer)  is  based  upon 
two  facts  :  (1)  a  floating  solid  sinks  until  it  displaces 
its  own  weight  of  the  liquid  in  which  it  floats  j  (2)  the 
volumes  of  two  liquids  displaced  by  the  same  floating 
solid  vary  inversely  as  their  densities. 

Experiment  4.  Take  a  prism  of  paraffined  wood  (Fig.  108) 
i  inch  square  and  5  inches  long,  with  a  quarter-inch  scale  on 
one  of  its  faces.  It  should  be  so  loaded  as  to  assume  a  vertical 
position  and  sink  just  4  inches  when  placed  in  water.  It  dis- 
places, therefore,  a  volume,  V  (i  X  -£-  X  4  =  1  cu.  in.),  of  water. 
Place  it  in  some  liquid  whose  specific  density  is  sought.  It 

displaces  a  volume,  V,  of  this  liquid.     Then  —f  =  the  specific 

density  of  the  given  liquid.     This  experi- 
l  ment  illustrates  the  principle  on  which  the 

densimeter  is  based. 


- 


FIG. 108. 


Instead  of  a  prism  of  wood,  a  glass  tube,  A  (Fig.  109), 
terminating  in  a  bulb  containing  shot  or  mercury,  is 
generally  used.  It  has  a  scale  of  specific  densities  on 
the  stem,  so  that  no  computation  is  necessary.  The 
experimenter  merely  places  it  in  the  liquid  to  be  tested, 
and  reads  the  specific  density  at  that  point  which  is 
at  the  surface  of  the  liquid. 

The  specific  density  of  a  gas  is  found  by  the  appli- 
cation of  the  same  principles  as  those  employed  in 
determining  that  of  a  liquid,  but  the  operation  is 
attended  with  peculiar  difficulties  (see  author's  "Prin- 
ciples of  Physics  ").  For  many  purposes  it  is  most  con- 
venient to  employ  hydrogen  gas  —  the  lightest  gas — as 
a  standard  for  gases.  Then,  assuming  the  density  of 
hydrogen  to  be  1,  that  of  air  is  14.7,  oxygen  16,  etc.  A 
cubic  centimeter  of  hydrogen  at  0°  C.  and  at  the  baro- 
metric pressure  of  760  mm.  weighs  at  Paris  0.0000895682  g.,  and  a  cubic 
centimeter  of  pure  dry  air  under  the  same  conditions  weighs  0.0012932  g. 


V 


FIG.  109. 


122  MOLAK    DYNAMICS. 


118.    Miscellaneous  Experiments, 

Experiment  5.  Find  the  volume  of  an  irregularly  shaped  body,  e.g. 
a  stone.  Find  its  loss  of  weight  in  water.  Keuiember  that  the  loss  of 
weight  is  precisely  the  weight  of  the  water  it  displaces,  and  that  the  vol- 
ume of  one  gram  of  water  is  one  cubic  centimeter. 

Experiment  6.  Find  the  capacity  of  a  test-tube,  or  of  an  irregularly 
shaped  cavity  in  any  body.  Weigh  the  body ;  then  fill  the  cavity  with 
water  and  weigh  again.  As  many  grams  as  its  weight  is  increased,  so 
many  cubic  centimeters  is  the  capacity  of  the  cavity. 

Experiment  7.  Float  a  sensitive  densimeter  in  water  at  about  60°  F. 
(15°  C.),  aad  in  other  water  at  about  180°  F.  (82°  C.).  Which  water  is 
denser  ? 

EXERCISES. 

1.  Can  you  by  placing  the  neck  of  a  bottle  in  your  mouth  suck  liquid 
out  of  the  bottle  ?     Explain. 

2.  What  is  the  weight  of  a  cubic  foot  of-  beechwood  ?     (Consult  the 
Table  of  Specific  Densities  in  the  Appendix.) 

3.  Into  what  space  must  you  compress  30  cu.  ft.  of  air  that  its  elastic 
force  may  be  made  five  times  as  great  ? 

4.  If  when  the  barometer  stands  at  760  mm.  a  cubic  meter  of  air  be 
forced  into  a  vessel  whose  capacity  is  1000  cc.,  what  pressure  will  be 
exerted  upon  its  interior  walls? 

5.  Why  do  ironclad  vessels  float  in  water  ? 

6.  A  block  of  ice  weighing  500  grams  floats  on  water,     (a)  What  vol- 
ume of  water  does  it  displace  ?     (b)  What  volume  of  ice  is  out  of  water  ? 

7.  Witt  ice  float  or  sink  in  alcohol  ?     (See  Table  of  Specific  Densities 
in  the  Appendix.) 

8.  Give  the  density  and  specific  density  of  gold,  cork,  and  alcohol. 

9.  The  effective  weight  of  a  stone  in  water  is  50  grams  ;  its  weight  in 
air  is  112  grams,     (a)  What  is  the  volume  of  the  stone  ?     (b)  What  is  its 
density  ? 

10.  How  many  cubic  centimeters  of  dry  air  at  760  mm.  and  at  0°  C. 
weigh  as  much  as  one  cubic  centimeter  of  water  at  4°  C.  ? 

11.  If  4  cu.  ft.  of  a  body  have  a  mass  of  180  pounds,  what  is  its  spe- 
cific gravity  ? 

,^/12.  How  much  will  one  k.  of  copper  weigh  in  water  ? 

13.  What  does  a  piece  of  lead  20  x  10  X  5  cm.  weigh  ? 

14.  How  much  does  a  cubic  foot  of  gold  weigh  ? 

15.  A  solid  body  weighs  10  pounds  in  air  and  6  pounds  in  water, 
(a)  What  is  the  weight  of  an  equal  volume  of  water  ?     (b)  What  is  its 
specific  gravity  ?     (c)  What  is  the  volume  of  the  body  ? 


EXERCISES. 


123 


16.  A  thousand-gram  bottle  filled  with  sea-water  requires  in  addition 
to  the  counterpoise  of  the  bottle  1026  grams  to  balance  it.     (a)  What  is 
the  specific  gravity  of  sea- water  ?     (6)  What  is  the  quantity  of  salt,  etc., 
dissolved  in  1000  grams  of  sea-water  ? 

17.  A  piece  of  cork  floating  on  water  displaces  2  pounds  of  water. 
What  is  the  weight  of  the  cork  ? 

18.  In  which  would  a  hydrometer  sink  farther,  in  milk  or  in  water  ? 

19.  What  metals  will  float  in  mercury  ? 

20.  (a)  Which  has  the  greater  specific  density,  water  at  10°  C.  or  water 
at  20°  C.?     (6)  If  water  at  the  bottom  of  a  vessel  could  be  raised  by 
application  of  heat  to  20°  C.,  while  the  water  near  the  upper  surface  had 
a  temperature  of  10°  C.,  what  would  happen  ? 

21.  A  block  of  wood  weighs  550  grams  ;  when  a  certain  irregularly 
shaped  cavity  is  filled  with  mercury  the  block  weighs  570  grams.     What 
is  the  capacity  of  the  cavity  ? 

22.  In  which  is  it  easier  for  a  person  to  float,  in  fresh  water  or  in  sea- 
water  ?     Why  ? 

23.  Fig.  110  represents  a  beaker  graduated  in  cubic  centimeters.    Sup- 
pose that  when  water  stands  in  the  graduate  at  50 

cc.,  a  pebble-stone  is  dropped  into  the  water,  and 
the  water  rises  to  75  cc.  (a)  What  is  the  volume  of 
the  stone  ?  (6)  How  much  less  does  the  stone  weigh 
in  water  than  in  air  ?  (c)  What  is  the  weight  of  an 
equal  volume  of  water  ? 

24.  If  a  piece  of  cork  be  floated  on  water  in  a 
graduate  and  displace  (i.e.  cause  the  water  to  rise) 
7cc. ,  what  is  the  weight  of  the  cork  ? 

s  25.  You  wish  to  measure  out  50  g.  of  sulphuric 
acid.  To  what  number  on  a  beaker  graduated  in 
cubic  centimeters  will  that  correspond  ? 

26.  A  measuring  beaker  contains  35  cc.  of  ether. 
What  is  the  weight  of  the  ether  ? 

27.  If  15  g.  of  salt  be  dissolved  in  1  liter  of  water  without  increasing 
the  volume  of  the  liquid,  what  will  be  the  specific  density  of  the  solution  ? 

28.  A  mass  whose  weight  in  air  is  30  g.  weighs  in  water  26  g.  and  in 
another  liquid  27  g.     What  is  the  specific  density  of  the  other  liquid  ? 

29.  Find  the  specific  gravity  of  .wax  from  the  following  data  :   weight 
of  a  given  mass  of  wax  in  air  is  80  g. ;  wax  and  sinker  displace  102.88  cc. 
of  water  ;  sinker  alone  displaces  14  cc. 

30.  A  boat  displaces  25  m.3  of  water.     How  much  does  it  weigh  ? 

31.  What  mass  of  alcohol  can  be  put  into  a  vessel  whose  capacity  is 
1  liter  ? 


FIG.  110. 


CHAPTER    IV. 
MOLECULAR   DYNAMICS.  -  HEAT. 


SECTION  I. 
THEORY  OF  HEAT. 

IN  the  preceding  pages  the  theory  of  heat  has  been  several 
times  anticipated  ;  we  are  now  better  qualified  to  judge  of 
its  validity. 

119.  Energy  of  Mechanical  Motion  Convertible  into  Heat, 

Experiment  1.  Place  a  tenpenny  nail  upon  a  stone,  and  hammer  it 
briskly  ;  it  soon  becomes  too  hot  to  be  handled  with 
comfort,  and  we  may  conceive  that  if  the  blows  were 
rapid  and  heavy  enough,  it  might  soon  become  red  hot. 
*  Rub  a  desk  with  your  fist,  and  your  coat  sleeve  with  a 
metallic  button  ;  both  the  rubbers  and  the  things  rubbed 
become  heated. 

You  observe  that  in  every  case  heat  is  gen- 
erated at  the  expense  of  work  or  mechanical 
energy  ;  i.e.  mechanical  energy  destroyed  becomes 
heat.  When  the  brakes  are  applied  to  the 
wheels  of  a  rapidly  moving  railroad  train,  its 
energy  is  converted  into  heat,  much  of  which 
may  be  found  in  the  wheels,  brake-blocks,  and 
rails. 

120.  Heat  Convertible  into  Mechanical 
Energy. 

Experiment  2.  Take  a  thin  glass  flask,  A  (Fig.  Ill),  half  fill  it  with 
water,  and  fit  a  cork  air-tight  into  its  neck.  Perforate  the  cork,  insert  a 
glass  tube  bent  as  indicated  in  the  figure,  and  extend  it  into  the  water. 
Apply  heat  to  the  flask ;  soon  the  liquid  rises  in  the  tube  and  flows  from 
its  upper  end 


FIG.  ill. 


KINETIC    THEORY    OF    HEAT.  125 

Here  heat  produces  mechanical  motion,  i.e.  it  does  work  in 
raising  a  mass  in  opposition  to  gravitation.  Every  steam 
engine  is  a  heat  engine,  i.e.  the  power  of  steam  is  due  to  its 
heat.  The  steam  which  leaves  the  cylinder  of  an  engine, 
after  it  has  set  the  piston  in  motion,  is  cooler  than  when  it 
entered. 

It  will  be  shown  hereafter  that  in  all  cases  when  work  is 
done  by  heat  without  waste  or  loss,  the  quantity  of  heat 
consumed  is  proportional  to  the  mechanical  work  done  ;  and, 
conversely,  by  the  performance  of  a  definite  quantity  of 
mechanical  work  an  equivalent  quantity  of  heat  may  be 
generated.  In  other  words,  there  is  a  definite  quantitative 
relation  between  heat  and  mechanical  work. 

If  heat  be  consumed,  and  mechanical  work  ther.eby  per- 
formed, we  are  justified  in  saying  that  heat  becomes  trans- 
formed into  mechanical  energy  ;  and,  conversely,  if  mechanical 
energy  be  expended  and  heat  thereby  produced,  we  may  say 
that  mechanical  energy  has  become  transformed  into  heat. 
This  has  lead  to  the  idea  that  heat  is  a  form  of  energy. 

121.  Kinetic  Theory  of  Heat.  A  hammer  descends  and 
strikes  an  anvil.  Its  motion  ceases,  but  the  anvil  is  not 
sensibly  moved  ;  the  only  observable  effect  produced  is  heat. 
Instead  of  a  motion  of  the  hammer  and  anvil,  there  is  now 
supposed  to  be  an  increased  vibratory  motion  of  the  molecules 
that  compose  the  hammer  and  anvil  —  simply  a  change  from 
mass  motion  to  molecular  motion.  Of  course  this  latter  motion 
is  invisible.  According  to  the  modern  view,  heat  is  but  a 
name  for  the  energy  of  vibration  of  the  molecules  of  a  body,  or, 
briefly,  HEAT  is  MOLECULAR  KINETIC  ENERGY.1  A  body  is 
heated  by  having  the  motion  of  its  molecules  quickened,  and 
cooled  by  parting  with  some  of  its  molecular  motion. 

1  As  late  as  the  beginning  of  the  nineteenth  century  heat  was  generally  regarded 
as  an  "  igneous  fluid"  sometimes  called  "  caloric."  Experiments  performed  by 
Count  Rumford,  Joule,  and  others  have  demonstrated  the  falsity  of  this  view  and 
have  led  to  the  adoption  of  tiie  kinetic  theory. 


126  MOLECULAR    DYNAMICS. 

SECTION    II. 

SOURCES    OF    HEAT. 

122.  Mechanical  Energy  a  Source  of  Heat.    As    heat  is 
energy,  so  all  heat  originates  in  some  form  of  energy,  i.e.  by 
the  transformation  of  some  other  form  of  energy  into  heat. 

In  the  preceding  section  it  was  shown  that  heat  may  be 
generated  at  the  expense  of  molar  motion,  i.e.  mass  motion 
checked  usually  results  in  increased  molecular  motion.  By 
friction,  by  compression,  by  percussion,  or  by  any  process  by 
which  mass  motion  is  arrested,  heat  is  mechanically  generated. 

123.  Chemical  Union  a  Source  of  Heat 

Experiment.  Take  a  glass  test-tube  half  full  of  cold  water,  and  pour 
into  it  one  fourth  its  volume  of  strong  sulphuric  acid.  The  liquid  almost 
instantly  becomes  so  hot  that  the  tube  cannot  be  held  in  the  hand. 

When  water  is  poured  upon  quicklime,  heat  is  rapidly 
developed.  The  invisible  oxygen  of  the  air  combines  with  the 
constituents  of  the  various  fuels,  such  as  wood,  coal,  oils,  and 
illuminating  gas,  and  gives  rise  to  what  we  call  combustion, 
by  which  a  large  amount  of  heat  is  generated.  In  all  such 
cases  the  heat  is  generated  by  the  combination  or  clashing 
together  of  molecules  of  substances  that  have  an  affinity  (i.e. 
an  attraction)  for  one  another. 

The  energy  possessed  by  fuels  and  all  substances  which  by 
chemical  union  generate  heat  is  called  the  potential  energy 
of  chemical  separation.  Chemical  affinity  converts  the  poten- 
tial energy  of  the  molecules  into  kinetic  energy  of  vibration, 
i.e.  into  heat. 

124.  The  Sun  as  a  Source  of  Energy.     The  sun  is  not  only 
a  direct  source  of  heat  but  it  is  also  the  source,  directly  or 
indirectly,  of  very  nearly  all  the  energy  employed  by  man 
in  doing  work.     The  growth  of  vegetation  is  maintained  by 
solar  light  and  heat.     Our  coal-beds,  the  results  of  the  deposit 


ORIGIN    OF    THE   SUN'S    HEAT.  127 

of  vegetable  matter,  are  vast  storehouses  of  the  sun's  energy 
rendered  potential  during  the  growth  of  the  plants  many 
ages  ago.  Animals  feed  upon  vegetable  matter  and  thereby 
appropriate  solar  energy.  Every  drop  of  water  that  falls  to 
the  earth  and  rolls  its  way  to  the  sea,  contributing  its  mite  to 
the  immense  water-power  of  the  earth,  and  every  wind  that 
blows,  derives  its  power  directly  from  the  sun. 

125.    Origin  of  the  Sun's  Heat  and  Energy.     This  has  been 

the  subject  of  much  speculation.  The  theory  of  combustion  or  any 
other  form  of  chemical  action  has  been  abandoned  by  physicists.  Two 
rival  theories,  viz.  the  meteoric  theory  and  the  contraction  or  compression 
theory,  now  offer  about  equal  claims  for  credence.  According  to  the 
former  theory,  the  heat  of  the  sun  originates  from  the  arrested  motion  of 
cosmical  bodies,  meteorites,1  that  fall  into  the  sun.  According  to  the 
latter  theory,  heat  is  generated  by  the  falling  in  of  the  sun  upon  itself, 
or  the  contraction  and  compression  due  to  the  mutual  attraction  between 
its  parts.  It  is  perhaps  not  amiss  to  attribute  the  heat  to  both  causes. 

It  is  the  conclusion  of  both  Professor  Langley  and  Lord  Kelvin  that 
the  temperature  of  the  sun's  photosphere  is  about  8000°  C.  The  temper- 
ature of  the  voltaic  arc  (§  374)  is  about  4000°  C. 


SECTION  III. 
TEMPERATURE   AND    THERMOMETRY. 

126.  Temperature  Denned.  The  words  warm,  hot,  cool,  cold, 
are  associated  in  our  minds  with  a  series  of  sensations  which 
correspond  to  a  series  of  states  of  matter  with  respect  to  heat. 
These  are  all  temperature  terms,  and  refer  to  the  state  of  an 
object  with  reference  to  heat.  When  the  quantity  of  heat  in 
a  body  increases,  its  temperature  is  said  to  rise;  and  when 
this  diminishes,  its  temperature  is  said  to  fall. 

1  The  intense  heat  of  meteorites  that  fall  to  the  earth  is  due  to  their  arrested 
mass  motion  on  entering  the  atmosphere.  Their  temperatures  are  almost  instantly 
raised  from  the  temperature  of  outer  space  (more  than  200  degrees  below  zero)  to  a 
temperature  above  that  of  the  melting  point  of  all  substances.  Their  speed  before 
entering  the  atmosphere  is  enormous.  In  the  outer  space  a  meteor  moves  farther  in 
one  second  than  the  fastest  express  train  moves  in  an  hour. 


128  MOLECULAR    DYNAMICS. 

If  body  A  when  brought  into  contact  with  body  B  tend 
to  impart  heat  to  it,  then  A  is  said  to  have  a  higher  tem- 
perature than  B.  Temperature  is  the  state  of  a  body  with 
reference  to  its  tendency  to  communicate  heat  to,  or  receive  heat 
from,  other  bodies.  The  direction  of  the  flow  of  heat  deter- 
mines which  of  two  bodies  has  the  higher  temperature.  If 
the  temperature  of  neither  body  rises  at  the  expense  of  the 
other,  then  both  have  the  same  temperature,  and  are  said  to 
be  in  thermal  equilibrium. 

Temperature  depends  on  the  average  kinetic  energy  of  the 
molecules.  The  temperature  of  a  body  increases  propor- 
tionally to  the  mean  square  of  the  velocity  of  vibration  of  its 
molecules. 

127.  Construction  of  a  Thermometer.     A  thermometer  is  an 
instrument  for  indicating  temperature.     It  consists  of  a  glass 
tube  of  uniform  capillary  bore,  terminating  at  one  end  in  a 
bulb,  the  bulb  and  a  part  of  the  tube  being  filled  with  mercury, 
and  the  space  in  the  tube  above  the  mercury  being  a  partial 
vacuum.     On  the  tube,  or  on  a  plate  of  metal  behind  the  tube, 
is  a  scale  to  show  the  hight  of  the  mercurial  column. 

If  a  thermometer  be  brought  into  intimate  contact  with  a 
body  whose  temperature  is  sought,  as,  for  instance,  a 'liquid 
into  which  it  is  plunged,  or  the  air  in  a  room,  the  mercury  in 
the  tube  rises  or  falls  1  until  it  reaches  a  certain  point,  at  which 
it  remains  stationary.  We  then  know  that  it  is  in  thermal 
equilibrium  with  the  surrounding  body.  Hence  the  reading, 
as  it  is  called,  of  the  thermometer  indicates  the  temperature 
not  only  of  the  mercury,  but  also  of  the  surrounding  body. 

128.  Graduation  of  Thermometers.     First,  the  bulb  of  a  thermom- 
eter is  placed  in  melting  ice  (Fig.  112)  and  allowed  to  stand  until  the  sur- 
face of  the  mercury  becomes  stationary,  when  a  mark  is  made  upon  the 
stem  at  that  point,  which  indicates  the  melting  point.     Then  the  instru- 

1  The  thermometer  primarily  indicates  changes  of  volume  ;  but  as  changes  of 
volume  in  this  case  are  caused  by  changes  of  temperature,  it  is  commonly  used  for 
the  more  important  purpose  of  indicating  temperature. 


GRADUATION  OF  THERMOMETERS. 


129 


FIG.  112 


ment  is  suspended  in  steam  rising  from  boiling  water  (Fig.  113),  so  that 

all  but  the  very  top  of  the  column  is  in  the  steam. 

The  bulb  is  placed  in  a  metallic  vessel,  M,  with  a  narrower  upper  part, 

A.     This  narrower  part  is  surrounded 

by  a  larger  part,  B.     By  observing  the 

arrows  it  is  seen  that  steam  surrounds 

the  inner  part,   and   thus  prevents  its 

cooling ;  it  escapes  by  the  tube  D.     The 

orifice  of  D  is  large  enough  to  allow  the 

steam  to  escape  freely,  and  thus  prevent 

a  pressure  inside  the  vessel  greater  than 

the   atmospheric  pressure.      To  guard 

against  such  a  contingency  a  pressure 

gauge,  m,  is  inserted  in  the  vessel.     The 

liquid  in  both  arms  of  the  gauge  must 

be  kept  at  the  same  level   throughout 

the   operation.     The   mercury  rises  in 

the  stem  of  the  thermometer  until  its      | 

temperature  becomes  the  same  as  that 

of  the  steam,  when  it  becomes  station- 
ary.    A  barometer  is  consulted,  and  due 

allowance  for  atmospheric  pressure  at  the  time  having  been  made,  a 
mark  is  placed  on  the  stem  to  indicate  the  boiling 
point.  This  boiling  point  is  the  temperature  of  steam 
at  a  pressure  of  760  mm.  of  mercury  at  0°  C.  Then 
the  space  between  the  two  points  found  is  divided 
into  a  convenient  number  of  equal  parts  called 
degrees,  and  the  scale  is  extended  above  and  below 
these  points  as  far  as  is  desirable. 

Two  methods  of  division  are  adopted  in  this  coun- 
try (see  a  and  b,  Fig.  114)  :  by  one,  the  space  is 
divided  into  180  equal  parts,  and  the  result  is  called 
the  Fahrenheit  scale,  from  the  name  of  its  designer ; 
by  the  other,  the  space  is  divided  into  100  equal 
parts,  and  the  resulting  scale  is  called  Centigrade, 
which  means  one  hundred  steps.  In  the  Fahrenheit 
scale,  which  is  generally  employed  in  the  United 

States  for  ordinary  household  purposes,  the  melting  and  boiling  points 

are  marked,  respectively,  32°  and  212°.     The  Centigrade  scale,  which  is 

generally  employed  by  scientists,  has  its  melting  and  boiling  points  more 

conveniently  marked,  respectively,  0°  and  100°.     A  temperature  below  0° 

in  either  scale  is  indicated  by  a  minus  sign  before  the  number.     Thus, 


FIG.  us. 


130 


MOLECULAR    DYNAMICS. 


—  12°  F.  indicates  12°  below  0°  (or  44°  below  the  melting  point  of  ice), 
according  to  the  Fahrenheit  scale.1  The  Fahrenheit  and  Centigrade 
scales  agree  at  —  40°,  but  diverge  both  ways  from  this  point. 

k  The  expansion  of  gases  is  made  the  basis  of  the 

standard  scale  of  temperatures,  to  which  all  other 
scales  are  referred  for  comparison  and  correction. 


100C 


129.  Conversion  from  One  Scale  to  the 
Other.  Since  100°  C.  =0=  180°  F.,  5°  C.  ^>= 
9°F.,  or  l°C.=o=f  of  1°F.  Hence,  to  con- 
vert Centigrade  degrees  into  Fahrenheit  de- 
grees, we  multiply  the  number  by  f  ;  and  to 
convert  Fahrenheit  degrees  into  Centigrade 
degrees,  we  multiply  by  f .  In  finding  the 
temperature  on  one  scale  that  corresponds  to 
a  given  temperature  on  the  other  scale,  it 
must  be  remembered  that  the  number  that 
expresses  the  temperature  on  a  Fahrenheit 
scale  does  not  express  the  number  of  degrees 
above  melting  point,  as  it  does  on  a  Centi- 
grade scale.  For  example,  52°  on  a  Fahren- 
heit scale  is  not  52°  above  melting  point,  but 
(52°  -  32°  =)  20°  above  it. 

Hence,  to  reduce  a  Fahrenheit  reading  to 
a  Centigrade  reading,  first  subtract  32  from  the 
given  number,  and  then  multiply  by  |.  Thus, 

|  (F.  -  32)  -  C. 

To  change  a  Centigrade  reading  to  a  Fahren- 
heit reading,  first  multiply  the  given  number  by  f,  and  then 
add  32.  Thus, 

C.  +  32  =  F. 


o° 


FIG.  114. 


1  The  0  of  the  Fahrenheit  scale  is  about  the  lowest  temperature  that  can  bo 
obtained  by  a  mixture  of  snow  and  salt,  and  was  formerly  thought  to  represent  the 
lowest  temperature  attainable.  The  first  practical  thermometer  was  constructed 
(1620)  by  Drebel,  a  Dutch  physician.  This  was  improved  (1749)  by  Fahrenheit  of 
Danzig.  Celsius  of  Upsala,  Sweden,  added  (1742)  the  scale  now  known  as  Centigrade. 


CALORIMETRY.  131 


EXERCISES. 

1.  Express  the  following  temperatures  of  the  Centigrade  scale  in  the 
Fahrenheit  scale  :  100°;  40°;  56°;  60°;  0°;  —  20°;  -  40°;  80°;  150°. 

NOTE.  In  adding  or  subtracting  32°,  it  should  be  done  algebraically.  Thus,  to 
change  —14°  C.  to  its  equivalent  in  the  Fahrenheit  scale:  §  x  (— 14)  =  —  25.2°; 
—  25.2°  +  32°=  6.8°,  the  required  temperature  in  the  Fahrenheit  scale.  Again,  to  find 
the  equivalent  of  24°  F.  in  the  Centigrade  scale  :  24  — 32  =  — 8;  —  8  x  f  =  —  4| ;  hence, 
24°  F.  is  equivalent  to  —4.4°  +  C. 

2.  Express  the  following  temperatures  of  the  Fahrenheit  scale  in  the 
Centigrade  scale  :  212°;  32°;   90°;   77°;  20°;    10°;    —10°;  -20°;  -40°; 
40°;   59°;  329°. 

3.  Explain  the  origin  of  the  heat  obtained  by  burning  coal. 

4.  In  what  does  the  value  of  coal  consist  ? 

5.  How  does  all  heat  originate  ? 

6.  (a)  Give  an  illustration  of  a  transformation  of  matter  ;  (6)  of  a  trans- 
formation of  energy. 

7.  The  absolute  zero  (§  141)  is  —  273°  C.;  what  is  this  on  the  Fahren- 
heit scale  ? 


SECTION   IV. 
CALORIMETRY. 

130.  Distinction  between  the  Questions  "How  Hot"  and 
"How  Much  Heat."  The  former,  like  the  question  "how 
sweet "  when  applied  to  a  solution  of  sugar,  is  answered 
only  relatively.  The  latter,  like  the  question  '.'how  much 
sugar  in  the  solution,"  is  answered  quantitively.  Sweet- 
ness and  temperature  are  independent  of  the  mass  of  the 
body.  A  pint  of  boiling  water  is  as  hot  as  a  gallon  of  the 
same  ;  but  the  latter  contains  eight  times  as  much  heat. 
Temperature  depends  on  the  average  kinetic  energy  of  the 
molecules.  Quantity  of  heat  is  the  product  of  the  average 
kinetic  energy  of  the  molecules  multiplied  by  the  number  of 
molecules.  The  quantity  of  heat  a  body  has  depends,  there- 
fore, upon  both  its  mass  and  its  temperature.  What  is  the 
meaning  of  the  statement  that  the  temperature  of  the  air 
is  20°  C.  ? 


132  MOLECULAR    DYNAMICS. 

131.  Thermal  Units.     A  thermal   unit  is  the  quantity  of 
heat  required  to  produce  a  definite  effect.     The  thermal  unit 
generally  adopted  is  the  calorie,  which  is  the  quantity  of  heat 
necessary  to  raise  one  kilogram  of  water  from  4°  to   5°  C. 
(Glazebrook).     The  thermal  unit  in  the  C.  G.S.  system  is  the 
gram-calorie,  sometimes  called  the  smaller  calorie,  which  is  the 
quantity  of  heat  required  to  raise  one  gram  of  water  from 
4°   to   5°  C.      The   operation   of    measuring    heat   is   called 
calorimetry. 

132.  Heat  Capacity;  Specific  Heat.     The   expression    heat 
capacity  applied  to  a  body  refers  to   the  quantity  of   heat 
necessary   to  raise   the  temperature  of  the   body   1°.     The 
expression  specific  heat  is  applied  only  to  some   particular 
substance,  and  refers  to  the  quantity  of  heat *  required  to  raise 
one  kilogram  of  that  substance  from  4°  to  5°  C.     It  is  appar- 
ent that  the  specific  heat  of  a  substance  is  the  heat  capacity 
of  1  unit  of  mass  of  that  substance. 

Experiment  1.  Mix  1  k.  of  water  at  0°  with  1  k.  at  20° ;  the  tempera- 
ture of  the  mixture  becomes  10°.  The  heat  that  leaves  1  k.  of  water 
when  it  falls  from  20°  to  10°  is  just  capable  of  raising  1  k.  of  water  from 
0°  to  10°. 

Experiment  2.  Take  (say)  300  g.  of  sheet  lead,  make  a  loose  roll  of 
it,  and  suspend  it  by  a  thread  in  boiling  water  for  about  five  minutes, 
that  it  may  acquire  the  same  temperature  (100°  C.)  as  the  water.  Remove 
the  roll  from  the  hot  water,  and  immerse  it  as  quickly  as  possible  in  300°  g. 
of  water  at  0°,  and  introduce  the  bulb  of  a  thermometer.  .  Note  the  tem- 
perature of  the  water  when  it  ceases  to  rise,  which  will  be  found  to  be 
about  3°  (accurately  3.3°  +).  The  lead  cools  very  much  more  than  the 
water  warms.  The  temperature  of  lead  falls  about  33°  for  every  degree 
an  equal  mass  of  water  is  warmed. 

From  the  first  experiment  we  infer  that  a  body  in  cooling 
a  certain  number  of  degrees  gives  to  surrounding  bodies  as 

1  Specific  heat  is  also  defined  as  the  ratio  of  the  quantity  of  heat  required  in  order 
to  raise  a  given  mass  of  a  substance  through  one  degree  to  the  quantity  required  in 
order  to  raise  an  equal  mass  of  water  through  one  degree.  Numerically  it  is  equal 
to  the  number  of  calories  required  to  raise  one  kilogram  of  the  substance  one 
degree. 


SPECIFIC   HEAT.  133 

much  heat  as  it  takes  to  raise  its  temperature  the  same 
number  of  degrees.  From  the  second  experiment  we  learn 
that  the  quantity  of  heat  that  raises  1  k.  of  lead  from  3.3° 
to  100°,  when  transferred  to  water,  can  raise  1  k.  of  water  only 
from  0°  to  3.3°.  Hence  we  conclude  that  equal  quantities 
of  heat,  applied  to  equal  masses  of  different  substances,  raise 
their  temperatures  unequally.  (See  Table  of  Specific  Heat, 
Appendix.) 

K  equal  masses  of  mercury,  alcohol,  and  water  receive  equal  quanti- 
ties of  heat,  the  mercury  will  rise  30°,  and  the  alcohol  nearly  2°,  for  every 
degree  the  water  rises.  From  this  we  infer  that,  to  raise  equal  masses 
of  each  of  these  substances  1°,  30  times  as  much  heat  is  required  for  the 
water  as  for  the  mercury,  and  twice  as  much  as  for  the  alcohol.  Since  a 
given  quantity  of  heat  affects  the  temperature  of  a  given  mass  of  water 
less  than  it  does  that  of  an  equal  mass  of  mercury  or  alcohol,  water  is 
said  to  have  greater  specific  heat  than  these  substances.  It  is  also  appar- 
ent that  a  given  mass  of  water  in  cooling  imparts  to  surrounding  bodies 
more  heat  than  the  same  mass  of  mercury  or  of  alcohol  would  impart  in 
cooling  the  same  number  of  degrees,  and  that  the  excess  is  in  proportion 
to  the  difference  in  specific  heat  between  the  substances. 

133.  Method  of  Measuring  Specific  Heat.  A  known  mass,  m 
(in  kilograms),  of  the  substance  of  which  the  specific  heat  is  required  is 
heated,  as  in  Experiment  2,  to  a  known  temperature  t\  (C.)  ;  then  it  is 
mixed  with  (or  immersed  in)  a  known  mass  of  water,  w2,  at  a  lower  tem- 
perature, t%,  and  as  soon  as  thermal  equilibrium  is  established  throughout, 
the  temperature  of  the  mixture  t  is  taken.  Let  s  represent  the  specific 
heat  of  the  substance  sought.  Then  the  quantity  of  heat  lost  by 
the  substance  is  m  s  (ti  —  t)  calories  ;  while  that  gained  by  the  water 
is  m2  (t  —  12)  calories.  Now  if  no  heat  be  lost  during  the  operation, 

m  s  (ti  —  t)  =  mz(t—  12),  whence  s  —  m<z  ,    —  fr-      For  example,  taking 

in  (ti  —  t) 

the  quantities  obtained  in  the  experiment  above,  we  find  for  lead 
(300  g.  _^  .8  k.)  .  =  T  =  -034  calorie. 


134.  Specific   Heat   of  the   Same   Substances  at  Different 
Temperatures  and  in  the  Three  States  of  Matter.     The   spe- 

cific heat  of  solids  and  liquids  usually  increases  slightly  with 


134  MOLECULAR    DYNAMICS. 

the  temperature,  and  diminishes  with  increase  of  density.  The 
specific  heat  of  water  at  0°,  40°,  and  80°  is,  respectively,  1, 1.003, 
and  1.0089  calories.  Substances  usually  have  a  higher  speci- 
fic heat  in  the  liquid  state  than  in  the  solid  or  gaseous  state. 
Thus,  water  has  nearly  double  the  specific  heat  of  ice,  and  a 
little  more  than  double  the  specific  heat  of  steam. 

135.  Great  Capacity  of  Water  for  Heat.  Water  requires 
more  heat  to  warm  it,  and  gives  out  more  in  cooling  through 
a  given  range  of  temperature  than  any  other  substance  except 
hydrogen.  The  quantity  of  heat  that  raises  a  kilogram  of 
water  from  0°  to  100°  C.  would  raise  a  kilogram  of  iron  from 
0°  to  800°  or  900°  C.,  or  above  a  read  heat.  Conversely,  a 
kilogram  of  water  in  cooling  from  100°  to  0°  C.  gives  out  as 
much  heat  as  a  kilogram  of  iron  gives  out  in  cooling  from 
about  900°  to  0°  C. 

"The  vast  influence  which  the  ocean  must  exert  as  a  moderator  of 
climate  here  suggests  itself.  The  heat  of  summer  is  stored  up  in  the 
ocean,  and  slowly  given  out  during  the  winter.  This  is  one  cause  of  the 
absence  of  extremes  in  an  island  climate." 

The  high  specific  heat  of  water  is  utilized  in  heating  buildings  by  hot 
water. 


EXERCISES. 

1.  The  specific  heat  of  mercury  is  .033  calorie.     Explain  this  state- 
ment. 

2.  What  is  the  heat  capacity  of  90  k.  of  mercury  ? 

3.  If  the  heat  yielded  by  1  k.  of  water  in  cooling  from  100°  to  0°  C. 
yj^were  employed  in  heating  100  k.  of  mercury  initially  at  20°,  to  what  tem- 
perature would  the  mercury  be  raised  ? 

4.  A  mass  of  700  g.  of  copper  at  98°  C.  put  into  800  g.  of  water  at  15° 
contained  in  a  copper  vessel  whose  mass  is  200  g.  raised  the  temperature 
of  the  water  to  21°.     Find  the  specific  heat  of  copper. 

5.  A  copper  ball  weighing  3  k. ,  taken  out  of  a  furnace  and  plunged 
into  10  k.  of  water  at  10°  C.,  heated  the  water  to  25°.     Find  the  tempera- 
ture of  the  furnace  [s.  h.  of  copper  =  .095].  -4ns.  551.3°  C. 


EXPANSION.  135 

6.  10  k.  of  a  certain  substance,  at  a  temperature  of  120°  C.,  is  mixed 
with  2  k.  of  water  at  20°  C.     The  temperature  of  the  mixture  is  25°  C. 
What  is  the  specific  heat  of  the  substance  ? 

7.  A  platinum  ball  whose  mass  is  900  g.  and  whose  temperature  is 
110°  C.  is  dropped  into  500  g.  of  water  at  20°.     To  what  temperature  will 
it  raise  the  water  ? 


SECTION  V. 
EFFECTS  OF  HEAT.   EXPANSION. 

136.  Experiments  Illustrating  Expansion  of  Solids,  Liquids, 
and  Gases. 

Experiment  1.  Take  two  brass  tubes,  one  of  a  size  that  will  just 
permit  it  to  enter  the  bore  of  the  other.  Heat  the  smaller  tube  ;  it  will  not 
in  its  expanded  state  enter  the  other.  Thrust  the  heated  tube  into  cold 
water  ;  its  temperature  falls,  and  it  now  enters  the  bore  of  the  other  tube. 
"  Heat  expands,"  but  "  cold  "  does  not  "  contract."  Cohesion,  when  a 
diminution  of  heat  (which  acts  as  a  repellent  force)  permits,  causes  a 
solid  or  liquid  body  to  contract.  Cold  is  a  term  of  negation  signifying 
merely  a  greater  or  less  deficiency  of  heat ;  it  is  not  an  entity,  and  hence 
it  cannot  be  the  direct  cause  of  any  phenomenon. 

Experiment  2.  Fig.  115  represents  a  thin  brass  plate  and  an  iron 
plate  of  the  same  dimensions  riveted  together  so  as  to  form  what  is  called 
a  compound  bar.  Place  the  bar  edgewise  ^ 

in  a  flame,  dividing  the  flame  in  halves    ^^^^J^ffiT* '  ••"••"' ""  • '";  •     -  • !  "aM*<i 
(one  half  on  each  side  of  the  bar)  so  FJG  llg 

that  both  metals  may  be  equally  heated. 

The  bar,  which  at  first  was  straight,  is  now  bent,  owing  to  the  unequal 
expansion  of  the  two  metals  on  receiving  equal  increments  of  temperature. 

Experiment  3.  Fit  stoppers  tightly  in  the  necks  of  two  similar  thin 
glass  flasks  (or  test-tubes),  and  through  each  stopper  pass  a  glass  tube 
about  60  cm.  long.  The  flasks  must  be  as  nearly  alike  as  possible.  Fill 
one  flask  with  alqohol  and  the  other  with  water,  and  crowd  in  the  stop- 
pers so  as  to  force  the  liquids  in  the  tubes  a  little  way  above  the  corks. 
Set  the  two  flasks  into  a  basin  of  hot  water,  and  note  that,  at  the  instant 
the  flasks  enter  the  hot  water,  the  liquids  sink  a  little  in  the  tubes,  but 
quickly  begin  to  rise,  until,  perhaps,  they  reach  the  top  of  the  tubes  and 
run  over. 

When  the  flasks,  first  enter  the  hot  water  they  expand,  and  thereby 
their  capacities  are  increased  ;  meantime,  the  heat  has  not  reached  the 


136 


MOLECtJLAK    DYNAMICS. 


liquids  to  cause  them  to  expand,  consequently  the  liquids  sink  momen- 
tarily to  accommodate  themselves  to  the  enlarged  vessel.  Soon  the  heat 
reaches  the  liquids,  and  they  begin  to  expand,  as  shown  by  their  rise  in 

the  tubes.     The  alcohol  rises  faster  than  the  water. 

Different  substances,  in  both  the  solid  and  the  liquid 

states,  expand  unequally  on  experiencing  equal  changes 

of  temperature. 

Experiment  4.  Take  a  dry  flask  like  that  used 
in  Experiment  3;  insert  the  end  of  the  tube  in  a 
bottle  of  colored  water  (Fig.  116),  and  apply  heat  to 
the  flask  ;  the  enclosed  air  expands  and  comes  out 
through  the  liquid  in  bubbles.  After  a  few  minutes 
withdraw  the  heat,  keeping  the  end  of  the  tube  in 
the  liquid ;  as  the  air  left  in  the  flask  cools,  its 
pressure  decreases,  and  the  water  is  forced  by 
atmospheric  pressure  up  the  tube  into  the  flask, 
?  and  partially  fills  it. 


FIG.  lie. 


137.  Expansion-coefficients.  The  expan- 
sion "which  attends  a  rise  of  temperature 
depends  not  only  upon  the  size  of  the  body,  and  upon  the 
number  of  temperature  degrees  through  which  it  is  heated, 
but  upon  a  quantity  peculiar  to  the  substance  itself,  called  its 
expansion-coefficient.  The  so-called  linear  expansion-coefficient 
is  the  increase  of  unit-length  per  degree  rise  of  temperature. 

Suppose  that  a  rod  of  length  Z,  at  0°  C.,  be  heated  through  t 
degrees,  so  that  its  length  becomes  ^  ;  then,  representing  the 
linear  expansion-coefficient  by  c,  we  have 


=  ±,  whence  I,  = 


ct). 


The  expression  1  +  ct,  called  the  expansion-factor,  is  evi- 
dently the  ratio  of  the  final  to  the  original  length.  Hence 
Jj  =  I  (1  +  ct)  ;  that  is,  multiplying  the  length  of  a  solid  at 
0°  0.  by  tfhe;  expansion-factor  gives  its  length  at  t  degrees 
above  zero»  Conversely,  dividing  its  length  at  t°  by  the- 
expansion-factor  gives  its  length  at  0°.  u 


ANOMALOUS    EXPANSION.  137 

In  the  expansion  of  fluids  we  have  to  do  only  with  increase 
of  volume,  called  volume  or  cubical  expansion.  A  volume 
expansion-coefficient  is  the  increase  of  unit  volume  per  degree 
rise  of  temperature.  This  is  approximately  3  c,  or  three  times 
the  linear  expansion-coefficient,  and  may  be  taken  as  such  for 
most  practical  purposes.  Likewise,  the  surface  or  superficial 
expansion-coefficient  is  approximately  2  c. 

Not  only  do  the  expansion-coefficients  of  liquids  and  solids 
vary  with  the  substance,  but  the  coefficient  for  the  same  sub- 
stance varies  with  the  temperature,  being  greater  at  high  than 
at  low  temperatures.  Hence,  in  giving  the  expansion-coeffi- 
cient of  any  substance  it  is  customary  to  give  the  mean 
coefficient  through  some  definite  range  of  temperature,  as  from 
0°  to  100°  C. 

It  is  found  that  the  expansion-coefficient  of  all  gases  is 
approximately  the  same  as  long  as  they  remain  true  gases, 
but  as  they  approach  the  vaporous  state  the  coefficient  changes 
rapidly. 

138.  Anomalous  Expansion  and  Contraction.  Water  pre- 
sents a  partial  exception  to  the  general  rule  that  matter 
expands  on  receiving  heat  and  contracts  on  losing  it.  If  a 
quantity  of  water  at  0°  C.,  or  32°  F.,  be  heated,  it  contracts 
as  its  temperature  rises,  until  it  reaches  4°  C.,  or  about  39°  F., 
when  its  volume  is  least,  and  it  therefore  has  its  maximum 
density.  If  heated  beyond  this  temperature  it  expands,  and 
at  about  8°  C.  its  volume  is  the  same  as  at  0°.  On  cooling^ 
water  reaches  its  maximum  density  at  4°  C.,  and  expands 
as  the  temperature  falls  below  that  point.  The  mass  of 
one  cubic  decimeter  of  pure  water  at  4°  C.  is  one  kilogram 
(§6). 

Water  is.  said  to  have  a  negative  expansion-coefficient 
between  0°  and  4°  C.,  or  between  32°  and  39.2°  F.  A  few 
other  substances,  such  as  india  rubber  and  iodide  of  lead,  con- 
tract when  heated,  and  have,  therefore,  negative  coefficients, 


138  MOLECULAR   DYNAMICS. 


EXERCISES. 

1.  How  does  rise  of  temperature  affect  the  density  of  a  body  ? 

2.  A  rod  of  copper  measures  10  feet  at  0°  C.  ;  its  length  at  100°  C.  is 
10.0159  feet.     Find  the  linear  expansion-coefficient  of  copper. 

3.  Two  rods,  one  of  brass,  the  other  of  wrought  iron,  are  each  10  feet 
long  at  0°  C.     Find  their  lengths  at  100°  C.     (See  Table  of  Expansion- 
coefficients  in  the  Appendix.) 

4.  The  volume  of  a  leaden  ball  at  60°  F.  is  100  cu.  in.    Find  its  volume 
at  the  boiling  point  of  water  (coefficient  of  linear  expansion  of  lead  on 
F.  scale  =  .0000157). 

5.  What  is  the  length  of  the  standard  platinum  meter  rod  at  80°  C.  ? 

6.  (a)  If  the  volume  of  a  brass  ball  at  10°  C.  be  840  cc.,  what  is  its 
volume  at  90°  ?     (b)  At  which  temperature  is  its  density  greater  ? 


SECTION   VI. 

KINETIC   THEORY    OF    MATTER.      LAWS   OF   GASEOUS 
BODIES.       ABSOLUTE   TEMPERATURE. 

139,  Kinetic  Theory  of  Matter.     The  theory  that  the  mole- 
cules composing  all  bodies  of  matter  are  in  perpetual  relative 
motion  is  called  the  kinetic  theory  of  matter.     This  theory 
claims   that   in    gases   the   molecules   are   so   far   separated 
from  one  another  that  their  motions  are  not  generally  influ- 
enced by  molecular  attractions.     Hence,  in  accordance  with 
the   first   law  of   motion,   the   molecules    of   gases   move   in 
straight   lines  and  with  uniform  velocity  until   they  collide 
with  one  another  or  strike  against  the  walls  of  the  containing 
vessel,  when,  in  consequence  of  their  perfect  elasticity,  they 
at  once  rebound  and  start  on  new  paths. 

140.  Pressure  of  a  Gas  Due  to  the  Kinetic  Energy  of  its 
Molecules.     Consider,  then,  what  a  molecular  storm  must  be 
raging  about  us,  and  how  it  must  beat  against  us  and  against 
every  exposed  surface.     According  to  the  kinetic  theory,  a 


PRESSURE    OF    GASES.  139 

gas  exerts  pressure  upon  the  receptacle  which  confines  it,  in 
consequence  of  the  incessant  impacts  of  the  molecules  of  the 
gas  upon  the  surfaces  against  which  the  gas  is  said  to  press, 
the  impulses  following  one  another  in  such  rapid  succession 
that  the  effect  produced  cannot  be  distinguished  from  constant 
pressure.  Upon  the  energy  of  these  blows,  and  upon  the 
number  of  blows  per  second,  must  depend  the  amount  of 
pressure.  But  we  have  learned  that  on  the  kinetic  energy  of 
the  individual  molecules  depends  that  condition  of  a  gas 
called  its  temperature  ;  so  it  is  apparent  that  the  pressure  of 
a  given  quantity  of  gas  varies  with  its  temperature.  Again, 
as  at  the  same  temperature  the  number  of  blows  per  second 
must  depend  upon  the  number  of  molecules  in  the  unit 
of  space,  it  is  apparent  that  the  pressure  varies  with  the 
density. 

141.  Absolute  Zero.  The  zeros  on  the  thermometric  scales 
which  we  have  hitherto  considered  are  provisional  and  arbi- 
trary. Absolute  zero  is  the  temperature  corresponding  to  a 
total  absence  of  heat.  At  the  absolute  zero  the  molecules 
must  be  supposed  to  be  at  rest.  At  this  temperature  gases 
(if  they  may  be  called  such)  exert  no  pressure,  and  occupy  no 
space  save  that  which  their  molecules  take  up  when  closely 
packed  together.  The  point  of  absolute  zero  is  independ- 
ent of  the  conventions  of  man.  It  is  a  point  of  absolute 
cold  or  total  absence  of  heat,  beyond  which  no  cooling  is 
conceivable. 

The  pressure  in  air  increases  or  diminishes  by  .00367  = 
(about)  ^\^  of  its  pressure  at  0°  for  each  Centigrade  degree  of 
rise  or  fall  of  temperature,  the  volume  being  maintained 
constant.  If  air  were  a  perfect  gas,  and  could  be  cooled  down 
to  —  273°  C.  (—  459.4°  F.),  it  would  cease  to  exert  pressure. 
The  reason  it  would  exert  no  pressure  is  that  its  particles 
would  possess  no  kinetic  energy,  no  motion.  This  is  assumed, 
therefore,  to  be  the  absolute  zero  of  temperature. 


140 


MOLECULAR    DYNAMICS. 


142.  Absolute  Temperature.  Absolute  temperature  is  that 
reckoned  from  the  absolute  zero,  or  —  273°  C.  Temperatures 
measured  from  absolute  zero  are  proportional  to  the  pressure 
of  a  theoretically  perfect  gas  of  constant  volume  and  density. 

The   absolute   tempera- 


||  ||     ture  (based  on  the  above 

o. 

,F.           II 

|I      theory)    of    any    body   is 

Tin  melts  233C  ' 

451°            506° 

878>*°    found  by   adding  273   to 

its   temperature    as    indi- 

cated by  a  Centigrade  ther- 

mometer, or  459.4  to  its 

Water  boils  100°  - 
Alcohol  boils  78°  - 

212°           373° 
172.4°         351° 

: 

5998°    temperature    as  indicated 

by  a  Fahrenheit  thermom- 

Ether  boils  35°  - 

95°             308° 

~ 

'    eter.   Figure  117  furnishes 

IcemeltsO0  - 

32&              273° 

~ 

a  comparative  view  of  both 

Mercury-freezes-38.8°   - 

-37.9°      234.20 

- 

421-5°    the  arbitrary  and  the  ab- 

solute thermometric  scales 

expressed  in  both  C  and  F 

Alcohol  freezes-J30.5°  " 

-202.9°     142.5° 

- 

256.5°    degrees. 

143.    Laws  of  Gaseous 

Lowest  temperature  yet  attained 
estimated  to  be  about-220'  ' 

-3G4°            530 

- 

95°      Masses.     It  follows,  from 

the  above  discussion,  that 

-273°  - 

FIG.  11' 

-459.4°           0° 

r. 

(1)  the  volume  of  a  given 

mass    of  gas   at    constant 

pressure   is  proportional  to    its   absolute   temperature;    i.e.  at 

v  (volume  of  a  given  mass  of  gas) 
constant  pressure     v        .  . 

t  (absolute  temperature) 


remains 


constant.     This  is  called  the  Law  of  Charles. 

(2)  The  pressure  of  a  given  mass  of  gas  ivhose  volume  is  kept 
constant  is  proportional  to  its  absolute  temperature. 

Boyle's  law  states  that  (3)  at  a  constant  temperature  the 
volume  of  a  given  mass  of  gas  is  inversely  proportional  to  its 
pressure  j  i.e.  the  product  of  its  pressure  and  it$  volume  is  con- 


EXERCISES.  141 

stant.  Now,  when  both  the  pressure  and  the  volume  vary  at 
the  same  time,  it  may  be  shown  that  (4)  the  product  of  the 
pressure  and  the  volume  of  a  given  mass  of  gas  is  proportional 
to  its  absolute  temperature.  A  gas  is  said  to  be  perfect  when  it 
perfectly  obeys  these  laws. 

We  may  also  state  the  fourth  law  as  follows  :  the  product  of  the  pres- 
sure and  the  volume  of  a  given  mass  of  gas  divided  by  its  absolute  tem- 
perature is  a  constant  quantity,  or 

PV-C 
T   ~ 

in  which  P  =  pressure,  V  =  volume,  T  —  absolute  temperature  of  a  given 
mass  of  gas,  and  C  =  a  constant  quantity,  the  value  of  which  depends  on 
the  gas  in  question. 


EXERCISES. 

1.  Find,  in  both  Centigrade  and  Fahrenheit  degrees,  the  absolute  tem- 
peratures at  which  mercury  boils  and  freezes. 

2.  At  0°  C.  the  volume  of  a  certain  mass  of  gas  under  a  constant 
pressure  is  500  cc.     (a)  What  will  be  its  volume  if  its  temperature  be 
raised  to  75°  C.  ?     (&)  What  will  be  its  volume  if  its  temperature  become 

-  20°  C.  ? 

3.  If  the  volume  of  a  mass  of  gas  at  20°  C.  be  200  cc.,  what  will  be  its 
volume  at  30°  C.  ?    Solution :  20°  C.  is  equivalent  to  (20  +  273)  293  abs. 
temp.  ;  then  293  :  303  :  :  200  :  206.8  cc.     Ans. 

4.  To  what  volume  will  a  liter  of  gas  contract,  if  cooled  from  30°  C.  to 

-  15°  C.  ? 

5.  One  liter  of  gas  under  a  pressure  of  one  atmosphere  will  have  what 
volume,  if  the  pressure  be  reduced  to  900  g.  per  square  centimeter,  while 
the  temperature  remains  constant  ? 

6.  The  volume  of  a  certain  mass  of  air  at  a  temperature  of  17°  C., 
under  a  pressure  of  800  g.  per  square  centimeter,  is  500  cc.     What  will  be 
its  volume  at  a  temperature  of  27°  C.,  under  a  pressure  of  1200  g.  per 
square  centimeter?     Solution:  17°  C.  is  equivalent  to  290°  abs.  temp.  ; 
27°  C.  is  equivalent  to  300°  abs.  temp.     Then  290  :  300  : :  500  X  800  :  x  X 
1200.     Whence  x  =  344.8  cc.     Ans. 

7.  If  the  volume  of  a  mass  of  gas  under  a  pressure  of  1  k.  per  square 
centimeter  at  a  temperature  of  0°  C.  be  1  liter,  at  what  temperature  will 


142  MOLECULAR   DYNAMICS. 

its  volume  be  reduced  to  1  cc.  under  a  pressure  of  200  k.  per  square  centi- 
meter ?    Ans.    54.6°  abs.  temp.,  or  —  218.4°  C. 

8.  If  a  cubic  foot  of  coal  gas  at  32°  F.,  when  the  barometer  is  at  30  in., 
have  a  mass  of  ^  lb.,  what  will  be  the  mass  of  an  equal  volume  at  68°  F., 
when  the  barometer  is  at  29  in.  ? 


SECTION  VII. 

EFFECTS   OF   HEAT.      FUSION. 

144,  Changes  of  Properties  in  Solids  Attending  Change  of 
Temperature.     "  Every  known  property  of  a  piece  of  matter, 
except  its  mass,  varies  with  variation  of  temperature."     Inas- 
much as  heat  tends  to  weaken  cohesion,  the  rigidity  and  the 
tenacity  of  solids  are  generally  lessened,  and  their  plasticity 
is  increased,  by  the  addition  of  heat. 

145.  Fusion.     Whether  a  given  substance  exist  in  a  solid, 
liquid,  or  gaseous  state  depends  upon  its  temperature  and 
the  pressure  it  is  under.     Solids  exposed  to  heat  generally 
liquefy  or  fuse.     Some,  like  ice  and  tin,  change  their  state 
abruptly  ;  others,  like  glass  and  wrought  iron,  become  plastic 
prior  to  liquefaction.     The  temperature  at  which  a  substance 
melts  is  called  its  fusion  point.     The  fusion  points  of  different 
substances  vary  greatly  :   that  of  alcohol  (— 130.5°  C.)  and 
that  of  iridium  (1950°  C.)  may  be  taken  as  extreme  examples. 
(See  Table  of  Melting  Points,  Appendix.) 

Experiment  and  experience  teach  that  (1)  the  melting  or 
solidifying  point  (they  are  approximately  the  same  for  the 
same  substance)  may  vary  widely  for  different  substances,  but  for 
the  same  substance  when  under  the  same  pressure  the  point  is 
invariable. 

(2)  The  temperature  of  a  solid  or  a  liquid  remains  constant  at 
the  melting  point  from  the  moment  that  melting  or  solidification 
begins  until  it  ceases. 


HEAT   OF   FUSION.  143 

Experiment  1.  Put  a  lump  of  ice  as  large  as  your  two  fists  into 
boiling  water  ;  when  it  is  reduced  to  about  £  its  original  size,  skim  it  out. 
Wipe  the  lump,  and  place  one  hand  on  it  and  the  other  on  a  lump  to 
which  heat  has  not  been  applied  ;  you  will  not  perceive  any  difference  in 
their  temperatures.  Under  ordinary  pressure  ice  cannot  be  made  warmer 
than  0°  C. 

146.  Heat  of  Fusion.     The   temperature   of   ice    remains 
constant  while  melting,  and,  generally,  heat  imparted  to  a 
melting    body   affects    its    temperature   very   little   if    any. 
Furthermore,  ice  and  other  solids  are  not  instantly  converted 
into  liquids  on  reaching  the  fusion  point,  but  absorb  a  quan- 
tity of   heat   proportionate  to  their   mass   before  fusion  is 
accomplished.     Inasmuch  as  none  of  the  heat  applied  during 
melting   raises  the  temperature  of   the  body,  the  question 
arises,   What  becomes  of  the  heat  applied  to  the  body?     The 
thermo-dynamical    theory   furnishes  -  the    only   satisfactory 
answer  to  this  important  question.     The  answer  is,  that  about 
all  the  heat  applied  to  a  body  during  fusion  is  consumed  in 
doing  internal  work,  as  it  is  called.     The  molecules  that  were 
held  firmly  in  their  places  by  molecular  forces  are,  during 
fusion,  moved  from  their  places,  and  so  work  is  done  against 
these   forces.     Heat,   the   energy  of  motion,   performs   this 
work,  and  is  thereby  converted  into  potential  energy.     The 
heat  which  disappears  in  melting  is  called  the  heat  of  fusion. 

If  a  large  quantity  of  heat  be  required  in  order  to  effect  the 
fusion  of  a  body,  it  must  be  inferred  that  the  amount  of  work 
done  is  proportionately  great.  It  is  fortunate  that  it  does 
require  much  heat  to  melt  moderately  small  masses  of  ice  and 
snow,  since  otherwise  on  a  single  warm  day  in  winter  all  the 
ice  and  snow  would  melt,  creating  most  destructive  freshets. 

147.  Measurement   of    the   Heat  of   Fusion.     Let    it    be 

required  to  find  approximately  the  quantity  of  heat  that 
disappears  during  the  melting  of  one  kilogram  of  ice.  This 
quantity  is  most  readily  determined  by  the  method  of  mixtures. 


144  MOLECULAR   DYNAMICS. 

Experiment  2.  Weigh  out  200  g.  of  dry  ice  chips  (dry  them  with  a 
towel),  whose  temperature  in  a  room  of  ordinary  temperature  may  be 
safely  assumed  to  be  0°  C.  Weigh  out  200  g.  of  boiling  water,  whose 
temperature  we  assume  to  be  100°  C.  Pour  the  hot  water  upon  the  ice, 
and  stir  it  until  the  ice  is  all  melted.  Test  the  temperature  of  the  result- 
ing liquid. 

Suppose  its  temperature  is  found  to  be  10°  C.  It  is  evident  that  the 
temperature  of  the  hot  water  in  falling  from  100°  to  90°  would  yield 
sufficient  heat  to  raise  an  equal  mass  of  water  from  0°  to  10°  C.  Hence, 
it  is  clear  that  the  heat  which  the  water  at  90°  yields  in  falling  from  90° 
to  10°  —  a  fall  of  80°  —  in  some  manner  disappears.  At  this  rate,  had 
you  used  1  k.  of  ice  and  1  k.  of  hot  water,  the  amount  of  heat  lost  would 
be  80  calories.  Careful  experiments,  in  which  suitable  allowances  are 
made  for  loss  or  gain  of  heat  by  radiation,  conduction,  absorption  by  the 
calorimeter,  etc.,  have  determined  that  SO  calories  of  heat  are  consumed 
in  melting  1  kilogram  of  ice. 

148.  Transformation  of  Heat  Reversible.  As  stated  at  the 
beginning  of  this  chapter,  work  is  transformable  into  heat, 
and,  as  stated  on  page  70,  potential  energy  is  transformed 
into  kinetic  energy  "by  the  return  of  the  particles  to  their 
original  positions  " ;  so  when  water  freezes  or  any  liquid  is 
resolidified,  the  potential  energy  reappears  as  heat. 

Water  in  freezing  undergoes  no  change  of  temperature  ;  hence,  if  heat 
be  developed  during  the  operation,  it  must  become  diffused  or  must  be 
"given  off"  in  order  to  allow  the  freezing  to  go  on.  As  the  diffusion  is 
necessarily  slow,  so  freezing  must  be  slow  ;  and  this  slow  development  of 
heat  and  its  immediate  dispersion  accounts  for  the  fact  that  we  are  sel- 
dom made  conscious  of  the  development  of  heat  during  solidification. 

Farmers  sometimes  turn  to  practical  use  this  well-known  phenomenon. 
Anticipating  a  cold  night,  they  carry  tubs  of  water  into  cellars  to  be 
frozen.  The  heat  generated  thereby,  although  of  a  low  temperature,  is 
sufficient  to  protect  vegetables  which  freeze  at  a  lower  temperature  than 
water. 

Heat  disappears  in  the  process  of  melting  ice  ;  and,  paradoxical  as  it 
may  seem,  heat  is  generated  by  freezing  water.  By  freezing  one  kilogram 
of  water  80  calories  of  heat  are  generated,  or  a  quantity  sufficient  to  raise 
the  temperature  of  one  kilogram  of  water  from  0°  to  80°  C.  Heat  of 
fusion  of  water  is  much  greater  than  that  of  other  liquids. 


EVAPORATION  ;    EBULLITION.  145 

SECTION   VIII. 

EFFECTS    OF    HEAT    CONTINUED.       VAPORIZATION. 

149.  Evaporation;  Ebullition,     The  process  of  converting 
a  liquid  into  a  vapor l  is  called  vaporization.     A  comparatively 
slow  vaporization,  which  takes  place  only  at  the  exposed  sur- 
face of  a   liquid,  is   called   evaporation.      A  rapid   process, 
which  may  take  place  throughout  the  liquid,  but  usually  is 
most  rapid  at  the  point  where  heat  is  applied,  is  called  boiling* 
or  ebullition.     Liquids  which   evaporate    readily   are   called 
volatile  liquids. 

150.  Boiling  Point  Dependent  upon  Pressure.     In   evapo- 
ration, molecules  fly  from  the  surface  of  the  liquid  and  mingle 
with  the  particles  of  the  air,  and  drive  only  a  certain  small 
portion  of  them  away.     In  boiling,  the  molecules  which  fly 
away  from  the  surface  drive  all  the  air  particles  away  a 
certain  distance.     Hence  the  vapor  of  a  boiling  liquid  must 
exert  a  pressure  at  least  as  great  as  the  atmospheric  pres- 
sure.    The  greater  the  external  pressure  to  be  overcome,  the 
greater  must  be  the  energy,  i.e.  the  higher  the  temperature,  of 
the  vapor.     When  the  vapor  of  a  liquid  exerts  a  pressure 
equal  to  that  of  the  atmosphere,  the  liquid  begins  to  boil,  and 
the  temperature  at  which  this   occurs  is  called  the  normal 
boiling  point  of  that  liquid. 

Experiment  1.  Half  fill  a  glass  flask  with  water.  Boil  the  water 
over  a  Bunsen  burner  ;  the  steam  will  drive  the  air  from  the  flask.  With- 
draw the  burner,  quickly  cork  the  flask  very  tightly,  and  plunge  the  flask 
into  cold  water,  or  invert  the  flask  and  pour  cold  water  upon  the  part 
containing  steam,  as  in  Fig.  118  ;  the  water  in  the  flask,  though  cooled 
several  degrees  below  the  usual  boiling  point,  boils  again  violently.  The 

1  A  vapor  is  a  gaseous  state  of  a  substance  which  at  ordinary  temperatures  exists 
as  a  solid  or  liquid. 

2  Boiling  is  the  agitation  of  a  liquid  produced  by  its  own  vapor,  which,  since  it  is 
lighter  than  the  surrounding  liquid,  tends  to  rise  rapidly  to  the  surface. 


146 


MOLECULAR   DYNAMICS. 


application  of  cold  water  to  the  flask  diminishes  the  pressure  of  the 
steam,  so  that  the  pressure  upon  the  water  is  diminished,  and  the  water 
boils  at  a  temperature  lower  than  its  normal  boiling  point. 

Experiment  2.  Place  a  test-tube  half  filled  with  ether  (Fig.  119) 
in  a  beaker  containing  water  at  a  temperature 
of  60°  C.  Although  the  temperature  of  the 
water  is  40°  below  its  boiling  point,  it  very 
quickly  raises  the  temperature  of  the  ether 
sufficiently  to  cause  it  to  boil  violently.  Intro- 
duce a  thermometer  into  the  test-tube,  and 
ascertain  the  boiling  point  of  ether. 

Experiment  3.  In  a  beaker  half  full  of 
distilled  water  suspend  a  thermometer  so  that 
the  bulb  will  be  covered  by  the  water  and  yet 
be  at  least  two  inches  above  the  bottom  of  the 
beaker.  Apply  heat  to  the  beaker,  and  observe 
any  changes  of  temperature  which  may  occur, 
both  before  and  after  boiling  begins.  The 
mercury  in  the  thermometer  rises  continuously 
until  the  water  begins  to  boil,  but  soon  after  (i.e.  as  soon  as  thermal 
equilibrium  between  the  mercury  and  water  is  estab- 
lished) it  ceases  to  rise,  thereby  showing  that  the  tem- 
perature of  the  water  remains  constant  notwithstanding 
heat  is  constantly  applied  to  it. 


FIG.  118. 


It  is  found  that  (1)  for  a  given  pressure  (for 
example,  that  of  the  atmosphere  at  760  mm.) 
every  liquid  has  a  definite  boiling  point ;  (2)  this 
boiling  point  remains  constant  after  boiling  has 
begun  ;  (3)  the  boiling  point  of  a  liquid  increases  with  the  pres- 
sure.    A  change    of   27  mm.   in   the    hight  of  a  barometric 
column  is  attended  with  a  change  of  about  1°  C.  in  the  boiling 
point  of  water  boiled  in  an  open  vessel. 

The  boiling  point  of  water  varies  with  the  altitude  of  places,  in  conse- 
quence of  the  change  in  atmospheric  pressure.  Roughly  speaking,  a 
difference  of  altitude  of  533  ft.  causes  a  variation  of  1°  F.  in  the  boiling 
point.  The  measurement  of  hights  by  means  of  the  boiling  point  is 
called  hypsometry.  A  hypsometer  is  simply  a  convenient  portable  appa- 
ratus for  boiling  water,  provided  with  a  thermometer  sensitive  to  (say) 
0.01°. 


EXERCISES.  147 


EXERCISES. 

1.  What  is  the  difference  between  a  body  that  has  heat  and  a  body 
that  has  no  heat  ? 

2.  What  is  the  temperature  of  a  body  that  has  no  heat  ? 

3.  What  quantity  of  water  at  90°  C.  is  required  to  melt  800  g.  of  ice  ? 
Ans.  711  g. 

4.  4.2  k.  of  steam  at  100°  C.  enters  a  radiator  in  a  room  and  is  con- 
densed into  a  liquid,  and  the  liquid  leaves  the  radiator  at  a  temperature 
of  97°  C.     What  quantity  of  heat  is  left  in  the  room  by  this  operation  ? 

5.  (a)  How  much  heat  is  required  to  convert  4  k.  of  ice  at  —  18°  C. 
into  steam  at  120°  C  ?     (6)  How  much  of  this  heat  is  changed  into 
"latent  heat"   (better,  potential  energy),  and  how  much  remains  as 
sensible  heat  ? 

6.  Let  900  g.  of  water  at  85°  C.  be  poured  upon  200  g.  of  ice  at  0°  C.  ; 
what  will  be  the  temperature  'of  the  water  after  the  ice  is  melted  ?    Ans. 
55°  C. 

151,  Heat  of  Vaporization.  Heat  that  is  consumed  in  the 
process  of  vaporization  is  called  heat  of  vaporization.  The 
quantity  of  heat  required  to  convert  a  gram  of  water  at 
100°  C.  into  steam  without  altering  its  temperature  (which  is 
the  same  as  the  quantity  of  heat  generated  by  the  condensa- 
tion of  one  gram  of  steam  at  100°)  is  called  the  heat  of 
vaporization  of  water. 

Let  it  be  required  to  find  the  heat  of  vaporization  of  water.     Find  the 
mass  in  grams  of  the  glass  beaker  or  calorimeter  C  (Fig.  120),  and  since 
it  will  receive  a  small  portion  of  the  heat  gen- 
erated by  the  condensation  of  the  steam,  find 
its  water  equivalent  by  multiplying  its  mass  by 
the  specific  heat  of  glass  (.177).     Represent  this 
quantity  by  mi.     Take  in  the  calorimeter  a  cer- 
tain known  mass,  Jf,  of  cold  water  at  a  known 
temperature,  t.      When  water  in  the  flask  A 
begins  to  boil,  introduce  the  end  of  the  delivery 
tube  B  into  the  water  in  C.     Screen  the  calorim- 
eter from  the  heat  of  the  lamp  and  flask  by  FIG.  120. 
means  of  a  board,  D.     The  steam  that  passes 

through  the  tube  is  condensed  on  entering  the  cold  water,  and  heats  the 
water.     When  a  considerable  portion  of  the  water  in  A  has  been  vapor- 


148  MOLECULAR    DYNAMICS. 

ized,  the  temperature  ti  of  the  water  in  C  is  taken  again,  and  the  contents 
of  the  calorimeter  are  again  weighed.  The  increase  m  in  the  mass  of 
water  in  C  is  the  mass  of  steam  which  has  been  condensed.  Let  L  be  the 
heat  of  vaporization.  Then  the  whole  quantity  of  heat  generated  by  the 
condensation  of  m  grams  of  steam  is  Lm,  and  the  quantity  of  heat  im- 
parted to  the  cold  water  in  falling  from  100°  to  ti°  is  m  (100  —  £1),  or  the 
total  quantity  of  heat  given  to  the  calorimeter  and  its  original  contents  is 
Lm  +  m  (100  —  ti).  The  heat  required  to  raise  the  calorimeter  and  its 
original  contents  from  t  to  t\  is  (M  +  mi)  (ti  —  t).  But  these  two  quanti- 
ties are  equal,  hence, 

Lm  +  m  (100  —  ti)  =  (M  +  nil)  (ti  —  t)  ; 

whence  L  =  (M  +  Wl)  (tl  ~  t}  ~  m 


Careful  experiments  have  determined  that  it  requires  536 
small  calories  of  heat  to  convert  one  gram  of  water  at  100° 
into  steam  at  100°,  or  536  calories  per  kilogram,  and  when 
the  process  is  reversed  536  calories  per  kilogram  of  steam  are 
generated  by  the  condensation. 

When  water  is  converted  into  steam,  the  larger  portion 
of  the  heat  which  disappears  is  consumed  in  separating  the 
molecules  so  far  that  molecular  attraction  is  no  longer  sen- 
sible ;  a.  small  portion  —  about  -fa  —  is  consumed  in  over- 
coming atmospheric  pressure.  The  amount  of  work  done  in 
boiling  is  very  great,  as  is  shown  by  the  amount  of  heat 
consumed.  Hence,  it  requires  a  long  time  for  the  water  to 
acquire  the  requisite  amount  of  heat.  This  is  a  protection 
against  sudden  and  disastrous  changes. 

Steam  is  a  most  convenient  vehicle  for  the  conveyance  of 
heat  of  vaporization,  i.e.  potential  energy,  from  the  boiler  to 
distant  rooms  requiring  to  be  heated.  For  example,  for  every 
kilogram  of  steam  condensed  in  the  pipes  of  the  radiator, 
536  calories,  or  heat  enough  to  raise  5.36  kilograms  (about 
12  pounds)  of  ice-water  to  the  boiling  point,  are  generated. 

152.  Distillation, 

Experiment  4.  Vessel  A  (Fig.  121),  called  a  condenser,  contains  a 
coil,  B,  called  a  worm,  of  copper  tubing,  terminating  at  one  extremity  at  a. 
The  other  end  of  the  tube  b  projects  through  the  side  of  the  vessel  near 


DISTILLATION. 


149 


FIG. 121. 


its  bottom.  Near  the  top  of  the  vessel  projects  another  tube,  F,  called 
the  overflow,  with  which  is  connected  a  rubber  tube,  H.  This  tube  con- 
veys the  warm  water  which  rises 
from  the  surface  of  the  heated  worm 
away  to  a  sink  or  other  convenient 
receptacle. 

Take  a  glass  flask,  C,  of  a  quart 
capacity,  and  fill  it  three  fourths 
full  of  pond  or  bog  water.  Con- 
nect the  flask  by  means  of  a  glass 
delivery-tube  with  the  extremity  a 
of  the  worm.  Heat  the  water  in  the 
flask  ;  as  soon  as  it  begins  to  boil, 
commence  siphoning  cold  water 
through  a  small  tube,  D,  from  an 
elevated  vessel,  E,  into  the  con- 
denser. Inasmuch  as  the  worm  is  constantly  surrounded  with  cold 
water,  the  steam  on  passing  through  it  becomes  condensed  into  a  liquid, 
and  the  liquid  (called  the  distillate)  trickles  from  the  extremity  b  into 
a  receiving  vessel.  The  distillate  is  clear,  but  the  water  in  the  flask 
acquires  a  yellowish  brown  tinge  as  the  boiling  progresses,  due  to  the 
concentration  of  impurities  (largely  of  vegetable  matter)  which  are  held 
in  suspension  and  solution  in  ordinary  pond  water.  The  apparatus  used 
is  called  a  still,  and  the  operation  distillation. 

When  a  volatile  liquid  is  to  be  separated  from  water,  —  for 
example,  when  alcohol  is  separated  from  the  vinous  mash  after 
fermentation, — the  mixed  liquid  is  heated  to  its  boiling 
point,  which  is  lower  than  that  of  water.  Much  more  of  the 
volatile  liquid  will  be  converted  into  vapor  than  of  the  water, 
because  its  boiling  point  is  lower.  Thus  a  partial  separation 
is  effected.  By  repeated  distillations  of  the  distillate,  a  95  per 
cent  alcohol  is  obtained. 

Crude  petroleum  consists  of  a  mixture  of  substances  having 
various  boiling  points.  The  separation  is  effected  by  slowly 
distilling  the  mixture,  with  a  thermometer  in  the  path  of  the 
vapor  ;  as  the  temperature  of  the  vapor  changes,  the  recepta- 
cles of  the  distillate  are  changed, 


150  MOLECULAR    DYNAMICS. 

SECTION   IX. 
METHODS   OF   PRODUCING   COLD   ARTIFICIALLY. 

153.  Artificial  Gold.     A  body  becomes  cold  only  by  losing 
heat.     As  heat  passes  only  from  warmer  to  colder  bodies,  it 
is  evident  that  the  temperature  of  a  body  cannot  fall  below 
that  of  surrounding  bodies  —  for  example,  below  the  tempera- 
ture of  other  bodies  in  the  same  room  —  by  the  natural  process 
of  imparting  heat  to  its  neighbors.     The  temperature  of  a 
body,  then,  can  be  reduced  below  that  of  its  neighbors  only 
by  some  artificial  means. 

The  fact  that  heat  is  consumed  in  the  conversion  of  solids 
into  liquids,  and  of  liquids  into  vapors,  is  turned  to  practical 
use  in  many  ways  for  the  purpose  of  producing  artificial  cold. 
The  following  experiments  will  illustrate  this  process. 

154.  Heat  Consumed  in  Dissolving-;  Freezing  Mixtures. 

Experiment  1.  Prepare  a  mixture  of  2  parts,  by  mass,  of  pulverized 
ammonium  nitrate  and  1  part  of  ammonium  chloride.  Take  about  75  cc. 
of  water  (not  warmer  than  8°  C.),  and  into  it  pour  a  large  quantity  of  the 
mixture,  stirring  it  while  dissolving  with  a  test-tube  containing  a  little 
cold  water.  The  water  in  the  test-tube  will  be  quickly  frozen.  A  finger 
placed  in  the  solution  will  feel  a  painful  sensation  of  cold,  and  a  ther- 
mometer will  indicate  a  temperature  of  about  —  10°  C. 

One  of  the  most  common  freezing  mixtures  consists  of 
3  parts  of  snow  or  broken  ice  and  1  part  of  common  salt. 
The  affinity  of  salt  for  water  tends  to  produce  liquefaction  of 
the  ice,  and  the  resulting  liquid  dissolves  the  salt,  both  opera- 
tions consuming  heat. 

155.  Heat  Consumed  in  Evaporation.     The  heat  consumed 
in  vaporization  is  greater  than  that  consumed  in  liquefaction ; 
for  example,  in  the  case  of  water  it  is  greater  in  the  ratio  of 
536  :  80.     Hence  evaporation  is  the  more  efficient  means  of 
producing  extremely  low  temperatures.     Whatever  tends  to 


FREEZING   MACHINES.  151 

hasten  evaporation  tends  to  accelerate  the  reduction  of  tem- 
perature. Rapidity  of  evaporation  Increases  with  the  tempera- 
ture,  the  extent  of  surface  exposed,  diminution  of  pressure,  and 
the  dryness  of  the  atmosphere.  Other  things  being  equal,  the 
more  volatile  the  liquid  employed  for  evaporation,  the  more 
rapid  the  consumption  of  heat.1 

Experiment  2.  Fill  the  palm  of  the  hand  with  ether ;  the  ether 
quickly  evaporates,  and  produces  a  sensation  of  cold. 

Experiment  3.  Place  water  at  about  40°  C.  in  a  thin,  porous  cup, 
such  as  is  used  in  electric  batteries,  and  the  same  amount  of  water  at  the 
same  temperature  in  a  glass  beaker  of  as  nearly  as  possible  the  same  size 
as  the  porous  cup.  Introduce  into  each  a  thermometer.  The  compara- 
tively large  amount  of  surface  exposed  by  means  of  the  porous  vessel 
will  so  hasten  the  evaporation  in  this  vessel,  that,  in  the  course  of  10  to  15 
minutes  a  very  noticeable  difference  of  temperature  will  be  indicated  by 
the  thermometers  in  the  two  vessels. 

In  warm  climates  water  is  frequently  kept  in  porous  earthen  vessels  in 
order  that  its  temperature  may  by  evaporation  be  kept  low  enough  to 
render  it  suitable  for  drinking. 

156.  Freezing  Machines.  The  production  of  artificial  cold  has 
become  an  important  industry.  The  impulse  was  given  by  the  need  of 
finding  means  of  preserving  meat  in  a  fresh  condition  during  its  transit 
to  foreign  countries  ;  also  of  preserving  perishable  articles  of  food,  e.g. 
fish,  eggs,  butter,  etc.,  in  our  storehouses. 

The  so-called  cold-air  freezing  machine  is  driven  by  a  steam  engine, 
and  its  working  parts  are  quite  similar  to  those  of  a  steam  engine.  In 
both  there  is  a  system  of  cylinders,  pistons,  and  valves,  and  a  working 
substance  which  undergoes  alternately  compression  and  expansion.  The 
working  substance  in  the  freezing  machine  is  air.  Power  furnished  by 
the  steam  engine  compresses  air  by  the  stroke  of  a  piston  in  the  com- 
pression cylinder.  This  cylinder  is  surrounded  by  a  jacket  in  which  cold 

1  Water  may  be  frozen  by  its  own  evaporation  in  the  receiver  of  an  air-pump  from 
which  the  air  (and  consequently  the  air  pressure)  is  removed.  By  reducing  the  pres- 
sure on  liquid  air  and  thus  causing  rapid  evaporation,  Dr.  Olszewski  cooled  helium, 
without  liquefying  it,  to  a  temperature  calculated  to  be  —264°  C.  under  a  pressure  of 
one  atmosphere.  The  same  experimenter  gives,  as  results  of  his  investigations,  the 
following :  Under  an  atmospheric  pressure,  oxygen  boils  at  —164° ;  specific  gravity  of 
the  liquid  1.124  at  — 181.4°.  Nitrogen  melts  at  —  214°,  boils  at  — 194.4° ;  specific  gravity 
.of  the  liquid  .885  at  —194°.  Hydrogen  boils  at  about— 240°.  In  most  instances  the 
temperature  is  taken  with  a  hydrogen  thermometer. 


152  MOLECULAR   DYNAMICS. 

water  constantly  circulates,  so  that  the  heat  generated  by  the  compres- 
sion of  the  air  is  taken  up  by  the  cold  water.  Thus  is  obtained  air  at 
ordinary  temperature  but  under  high  pressure. 

If  the  air,  when  the  pressure  is  removed,  is  allowed  to  expand  into 
a  vacuum,  no  work  will  be  done  by  the  air  and  (as  proved  by  Joule) 
no  change  of  temperature  takes  place.  But  in  this  machine  the  air  in 
expanding  drives  a  piston  in  an  expansion  cylinder  and  mechanical  work 
is  done  at  the  expense  of  the  heat  of  the  expanding  air.  This  piston  is 
connected  with  the  piston  rod  of  the  steam  engine  in  such  a  way  as  to 
lighten  the  work  of  the  latter. 

By  means  of  this  expansion  the  air  is  readily  cooled  to  —  50°  F. 
Articles  to  be  kept  cool  are  placed  in  large  chambers,  the  walls  of  which 
are  double,  the  interspace  being  filled  with  charcoal,  a  non-conducting 
material.  A  stream  of  intensly  cold  air  is  injected  into  the  chamber  at 
each  stroke  of  the  piston  of  the  expansion  cylinder,  and  the  temperature 
of  the  chamber  is  thus  kept  constantly  near  the  freezing  point. 

The  ammonia  machine  is  another  type  of  freezing  machine.  In  this 
the  frigorific  effect  is  due  first  to  the  heat  consumed  by  the  vaporization 
of  liquid  ammonia  which  has  been  condensed  under  high  pressure  ;  and, 
secondly,  as  in  the  air  machine,  to  the  expansion  of  the  vapor.  In  this 
machine  the  expansion  of  the  vapor  takes  place  in  long  coils  of  tubing 
placed  in  a  bath  of  brine  which  has  a  low  freezing  point.  From  this 
bath  the  cold  brine  is  driven  by  pumps  through  a  system  of  tubes  to 
places  where  refrigeration  is  required.  In  this  manner  ice  is  manufac- 
tured artificially  in  the  summer  season. 


SECTION   X. 
HYGROMETRY. 

157.  Dew-point.  Hygrometry  treats  of  the  state  of  the  air 
with  regard  to  the  water  vapor  it  contains.  A  given  space,  e.g. 
a  cubic  meter  (it  matters  little  whether  there  is  air  in  the  space 
or  whether  it  is  a  vacuum),  can  hold  only  a  limited  quantity  of 
water  vapor.  This  quantity  depends  upon  the  temperature. 
The  capacity  of  a  space  for  water  vapor  increases  rapidly 
with  the  temperature,  being  nearly  doubled  by  a  rise  of  10°  C. 
On  the  other  hand,  if  air  containing  a  given  quantity  of  water 
vapor  be  cooled,  it  will  continually  approach  and  finally  reach 


DEW-POINT.  153 

saturation,  since  the  lower  the  temperature,  the  less  the  capac- 
ity for  water  vapor.  It  is  evident  that  air  saturated  with 
vapor  cannot  have  its  temperature  lowered  without  the  con- 
densation of  some  of  the  vapor  into  a  liquid,  which  will 
appear,  according  to  location  and  condition  of  objects  within 
it,  as  dew,  fog,  or  cloud.  The  temperature  at  which  this 
condensation  occurs  is  called  the  dew-point  for  air  containing 
this  proportion  of  water  vapor.  The  dew-point  may  be 
denned  as  the  temperature  of  saturation  for  the  quantity  of 
water  vapor  actually  present  in  the  air.  The  greater  the 
quantity  of  water  vapor  present  in  the  air,  the  higher  is  its 
dew-point.  Capacity  for  water  vapor  depends  upon  tempera- 
ture ;  dew-point  depends  upon  the  quantity  of  vapor  present. 
If  the  existing  temperature  be  far  above  dew-point,  it 
indicates  that  the  air  can  contain  much  more  vapor  than  there 
is  in  it  at  the  time,  and  the  air  is  said  to  be  dry  and  to  have 
a  low  dew-point.  If  the  temperature  of  the  air  be  little 
above  dew-point,  the  air  is  said  to  be  humid  and  to  have  a 
high  dew-point,  which  means  that  it  can  hold  but  little  more 
vapor.  The  sensation  of  dryness  experienced,  especially  in 
rooms  heated  artificially,  does  not  depend  upon  the  absolute 
quantity  of  water  vapor  present  per  cubic  foot. 

The  heat  of  a  stove,  for  instance,  dries  the  air  of  a  room  without  de- 
stroying any  of  its  water  vapor.  In  such  a  room  the  lips,  tongue,  throat, 
and  skin  experience  a  disagreeable  sensation  of  dryness,  owing  to  the 
rapid  evaporation  which  takes  place  from  their  surfaces.  This  should  be 
taken  as  nature's  admonition  to  keep  water  in  the  stove  urns,  and  in 
tanks  connected  with  furnaces. 

The  quantity  of  water  vapor  present  in  the  air  is  expressed  either 
(1)  by  the  mass  of  vapor  per  unit  of  volume  ;  or  (2)  by  the  ratio  between 
the  quantity  actually  present  and  that  which  would  be  present  if  the  air 
were  saturated  at  the  temperature  of  observation.  The  latter  is  the  more 
common  and  more  useful  method,  and  this  ratio  is  called  the  relative 
humidity,  or  simply  "  humidity  "  of  the  air.  It  is  expressed  in  percent- 
ages. Thus,  "relative  humidity  =  76  per  cent,  or  0.75,"  denotes  that 
the  air  contains  three  fourths  the  quantity  of  water  vapor  required  to 
saturate  it  at  the  present  temperature. 


154  MOLECULAR    DYNAMICS. 

SECTION   XI. 
DIFFUSION   OR   TRANSFERENCE   OF   HEAT. 

158.  Three  Processes  of  Diffusion.     There  is  always  a  tend- 
ency  to    equalization   of  temperature;   that   is,    heat   has   a 
tendency  to  pass  from  a  warmer  body  to  a  colder,  or  from  a 
warmer  to  a  colder  part  of  the  same  body,  until  there  is  an 
equality  of  temperature. 

There  are  commonly  recognized  three  processes  of  diffusion 
of  heat  —  conduction,  convection ,  and  radiation. 

159,  Conduction. 

Experiment  1.  Place  one  end  of  a  wire  about  10  inches  long  in  a 
lamp  flame,  and  hold  the  other  end  in  the  hand.  Heat  gradually  travels 
from  the  end  in  the  flame  toward  the  hand.  Apply  your  fingers  succes- 
sively at  different  points  nearer  and  nearer  the  flame  ;  you  find  that  the 
nearer  you  approach  the  flame  the  hotter  the  wire  is. 

The  flow  of  heat  through  an  unequally  heated  body,  from 
places  of  higher  to  places  of  lower  temperature,  is  called 
conduction;  the  body  through  which  it  travels  is  called  the 
conductor.  The  molecules  of  the  wire  in  the  flame  have  their 
motion  quickened;  they  strike  their  neighbors  and  quicken 
their  motion  ;  the  latter  in  turn  quicken  the  motion  of  the 
next ;  and  so  on,  until  some  of  the  motion 
is  finally  communicated  to  the  hand,  and 
creates  in  it  the  sensation  of  heat. 


Experiment  2.     Fig.  122  represents  a  board  on 
which  are  fastened,  by  means  of  staples,  four  wires  : 
(1)  iron,  (2)  copper,  (3)  brass,  and  (4)  German  silver. 
FIG  122  Place  a  lamp  flame  where  the  wires  meet.     In  about 

a  minute  run  your  fingers  along  the  wires  from  the 
remote  ends  toward  the  flame,  and  see  how  near  you  can  approach  the 
flame  on  each  without  suffering  from  the  heat.  Make  a  list  of  these 
metals,  arranging  them  in  the  order  of  their  conductivity. 


CONVECTION   IN/C^ESf.  T!    [.  —y^j        155 

You  learn  that  some  substances\Qonduct  heat,  much  more 
rapidly  than  others.  The  former  arecaf fed:  Tfood  conductors, 
the  latter  poor  conductors.  Metals  are  the  best  conductors, 
though  they  differ  widely  among  themselves. 

Experiment  3.     Nearly  fill  a  test-tube  with  water,  and  hold  it  some- 
what inclined  (Fig.  123),  so  that  a  flame  may  heat  the  part  of  the  tube 
near  the  surface  of  the  water.    Do  not  allow 
the  flame  to  touch  the  part  of  the  tube  that 
does  not  contain  water.     The  water  may 
be  made  to  boil  near  its  surface  for  several 
minutes  before  any  change  of  the  tempera- 
ture at  the  bottom  will  be  perceived. 

Liquids,  as  a  class,  are  poorer  con- 
ductors than  solids.  Gases  are  much 
poorer  conductors  than  liquids. 

It  is  difficult  to  discover  that  pure,  dry  FIG.  123. 

air  possesses  any  conducting  power.     The 

poor  conducting  power  of  our  clothing  is  due  partly  to  the  poor  conduct- 
ing power  of  the  fibers  of  the  cloth,  but  chiefly  to  the  air  which  is 
confined  by  it.  Loose  garments,  and  garments  of  loosely  woven  cloth, 
inasmuch  as  they  hold  a  large  amount  of  confined  air,  furnish  a  good 
protection  from  heat  and  cold.  Bodies  are  surrounded  with  bad  con- 
ductors in  order  to  retain  heat  when  their  temperature  is  above  that 
of  surrounding  objects,  and  to  exclude  it  when  their  temperature  is  below 
that  of  surrounding  objects.  In  the  same  manner  the  confined  air 
between  double  windows  and  double  doors  protects  from  cold. 

160.  Convection  in  Gases.  Conduction  takes  place  gradu- 
ally and  slowly  at  best  from  particle  to  particle,  the  body 
and  its  particles  being  relatively  at  rest.  Convection  takes 
place  when  the  body  moves,  or  when  there  is  relative  motion 
between  its  parts,  the  heat  in  either  case  being  conveyed  from 
one  place  to  another. 

Experiment  4.  Cover  a  candle  flame  with  a  glass  chimney  (Fig. 
124),  blocking  the  latter  up  a  little  way  so  that  there  may  be  a  circula- 
tion of  air  beneath.  Hold  smoking  touch-paper  near  the  bottom  of  the 
chimney  ;  the  smoke  seems  to  be  drawn  with  great  rapidity  into  the 


156 


MOLECULAR    DYNAMICS. 


chimney  at  the  bottom  ;  in  other  words,  the  office  of  the  chimney  is  to 
create  what  is  called  a  draft  of  air.  Notice  whether  the  combustion  takes 
place  any  more  rapidly  with  the  chimney  than  without  it. 

Experiment  5.  Place  a  candle  within  a  circle  of  holes  cut  in  the 
cover  of  a  vessel,  and  cover  it  with  a  chimney,  A  (Fig.  125).  Over  an 
orifice  in  the  cover  place  another  chimney,  B.  Hold  a  row  of  smoking 
touch-paper  over  B.  The  smoke  descends  this  chimney,  and  passes 
through  the  vessel  and  out  at  A.  This  illustrates  the  method  often 
adopted  to  produce  a  ventilating  draft  through  mines.  Let  the  interior 
of  the  tin  vessel  represent  a  mine  deep  in  the  earth,  and  the  chimneys 
two  shafts  sunk  to  opposite  extremities  of  the  mine.  A  fire  kept  burning 
at  the  bottom  of  one  shaft  will  cause  a  current  of  air  to  sweep  down  the 
other  shaft,  and  through  the  mine,  and  thus  keep  up  a  circulation  of 
pure  air  through  the  mine. 


FIG. 124. 


FIG.  125. 


The  cause  of  the  ascending  currents  is  evident.  Air,  on  becoming 
heated,  expands  rapidly  and  becomes  much  rarer  than  the  surrounding 
colder  air  ;  hence  it  rises,  much  like  a  cork  in  water,  while  cold  air  pours 
in  laterally  to  take  its  place.  In  this  manner  winds  are  created.  Sea 
and  land  breezes  are  convection  currents. 

161.  Ventilation.  Intimately  connected  with  the  topic 
convection  is  the  subject  (of  vital  importance)  ventilation, 
inasmuch  as  our  chief  means  of  securing  the  latter  is  through 
the  agency  of  the  former.  The  chief  constituents  of  our 
atmosphere  are  nitrogen  and  oxygen,  with  varying  quantities 
of  water  vapor,  argon,  carbon  dioxide  gas,  ammonia  gas,  nitric 
acid  vapor,  and  other  gases.  The  atmosphere  also  contains  in 


VENTILATION. 


157 


a  state  of  suspension  varying  quantities  of  small  particles  of 
free  carbon  in  the  form  of  smoke,  microscopic  organisms,  and 
dust  of  innumerable  substances.  All  of  these  constituents 
except  the  first  four  are  called  impurities.  Carbon  dioxide 
is  the  impurity  that  is  usually  the  most  abundant  and  most 
easily  detected ;  so  it  has  come 
to  be  taken  as  the  measure  of 
the  purity  of  the  atmosphere, 
though  not  itself  the  most  dele- 
terious constituent.  Its  chief 
harm  arises  from  its  diluent 
effect  upon  the  life-giving  oxy- 
gen. Pure  outdoor  air  contains 
about  4  parts  of  carbon  dioxide 
by  volume  in  10,000.  If  the 
quantity  rise  to  10  parts,  the 
air  becomes  unwholesome. 

The  quantity  of  fresh  air  intro- 
duced into  an  occupied  room  should 
be  great  enough  to  dilute  the  impuri- 
ties till  they  are  harmless.  An  adult 
makes  about  18  respirations  per  min- 
ute, expelling  from  his  lungs  at  each 
expiration  about  500  cc.  of  air,  over 

4  per  cent  of  which  is  carbon  dioxide.  FlG  126 

At  this  rate,  about  9  cubic  decimeters 

of  air  per  minute  become  unfit  for  respiration  ;  and  to  dilute  this  suffi- 
ciently, good  authorities  say  that  about  100  times  as  much  fresh  air  is 
needed  ;  or,  for  proper  ventilation,  about  a  cubic  meter  of  fresh  air  per 
minute  is  needed  for  each  person;  i.e.  in  British  measures,  2,000  cubic 
feet  per  hour. 

Fig.  126  represents  a  scheme  for  heating  a  room  by  steam,  and  venti- 
lating it  by  convection.  Steam  is  conveyed  by  a  pipe  from  the  boiler  to 
a  radiator  box  just  beneath  the  floor  of  the  room.  The  air  in  the  box 
becomes  heated  by  contact  with  and  radiation  (§  163)  from  the  coil  of  pipe 
in  the  box,  and  rises  through  a  passage  opening  into  the  room  by  means  of 
a  register  near  the  floor  at  C,  a  supply  of  pure  air  being  kept  up  by  means 


158 


MOLECULAR    DYNAMICS. 


of  a  tubular  passage  opening  into  the  box  from  the  outside  of  the  build- 
ing. Thus  the  room  is  furnished  with  pure  warm  air,  which,  mingling 
with  the  impurities  arising  from  the  respiration  of  its  occupants,  serves 
to  dilute  them  and  render  them  less  injurious.  At  the  same  time  the 
warm  and  partially  vitiated  air  of  the  room  passes  through  the  open  ven- 
tilator A  into  the  ventilating  flue  and  escapes,  so  that  in  a  moderate 
length  of  time  a  nearly  complete  change  of  air  is  effected.  No  system  of 
ventilation  dependent  wholly  on  convection  is  adequate  properly  to  ven- 
tilate crowded  halls ;  air  is  too  viscous  and  sluggish  in  its  movements. 
In  such  cases  ventilation  should  be  assisted  by  some  mechanical  means, 
such  as  a  blower  or  fan,  driven  by  steam  or  water  power. 

162,  Convection  in  Liquids. 

Experiment  6.  Fill  a  small  (6-ounce)  thin  glass  flask  with  boiling 
hot  water  colored  with  a  teaspoonful  of  ink,  stopper  the  flask,  and  lower 
it  deep  into  a  tub,  pail,  or  other  large  vessel  filled 
with  cold  water  (Fig.  127).  Withdraw  the  stopper, 
and  the  hot,  rarer,  colored  water  will  rise  from  the 
flask,  and  the  cold  water  will  descend  into  the  flask. 
The  two  currents  passing  into  and  out  of  the  neck  of 
the  flask  are  easily  distinguished.  The  colored  liquid 
marks  distinctly  the  path  of  the  heated  convection 
currents  through  the  clear  liquid,  and  makes  clear 
the  method  by  which  heat,  when  applied  at  the 
bottom  of  a  body  of  liquid,  becomes  rapidly  diffused 
through  the  entire  mass,  notwithstanding  that  liquids 
are  poor  conductors. 

By  similar  convection  currents  the  warming  of 
buildings  by  hot  water  is  effected.  Water  heated  in 
a  boiler  in  the  basement  rises  through  pipes  to  the 
radiators  in  the  rooms  above  ;  there  it  gives  heat  to  the  air  of  the  room, 
and,  after  being  thus  cooled,  it  returns  by  other  pipes  leading  from  the 
radiators  to  the  boiler.  Ocean  currents,  e.g.  the  gulf  stream,  are  convec- 
tion currents.  The  warmer  portions  of  the  waters  flow  away  from  the 
tropical  toward  the  polar  latitudes,  while  at  greater  depths  the  cold  waters 
of  high  latitudes  flow  back  toward  the  tropics. 

Liquids  are  also  cooled  by  convection  currents.  When  the  air  above 
the  surface  of  a  pond,  for  instance,  is  cooler  than  the  surface  water,  the 
latter  gives  heat  to  the  former,  cools,  becomes  denser,  and  sinks.  Mean- 
while, the  warmer  and  rarer  water  below  rises,  and  in  this  way  the  entire 
body  is  kept  at  an  approximately  uniform  temperature  until  it  reaches 
4°  C. ,  at  which  point  convection  ceases. 


FIG. 127. 


RADIATION.  159 

163.  Radiation.     In  radiation  a  hotter   body  loses  heat, 
and  a  colder  body  is  warmed,  through  the  transmission  of 
undulatory  motion  in  a  medium  called  the  ether,  which  is  not 
itself  heated  thereby.     It  is  neither  a  mass  nor  a  molecular 
transference  of  heat ;  in  fact,  heat  itself  is  not  transferred 
by  radiation  at  all.     Heat  generates  radiation  (ether-waves) 
at   one   place,  and   the   body   which    obstructs  these  waves 
transforms  the  energy  of  their  motion,  or,  as  it  is  commonly 
called,  radiant  energy,  into  heat.     In  this  manner  the  earth 
is  heated  by  the  sun,  though  no  heat  passes  between  them. 
In   this  manner    radiant   energy  passes   through   glass   and 
slabs   of  ice  without  heating   them  much,   since  they  offer 
little  obstruction  to  the  passage  of  ether-waves.     All  bodies 
emit  radiant  energy,   and  there  is  an   exchange  of  energy 
between  bodies  by  radiation   going  on  at  all   times.      This 
mode  of  transmission  of  energy  is  the  most  important  of  all, 
and  will  be  treated  fully  in  a  future  chapter. 

SECTION   XII. 
THERMO-DYNAMICS. 

164.  Thermo-dynamics  Denned.    Thermo-dynamics  treats  of 
the  relation  between  heat  and  mechanical  work.     One  of  the 
most  important  discoveries  in  science  is  that  of  the  equivalence 
of  heat  and  work;  that  is,  that  a  definite  quantity  of  mechanical 
work,  when  transformed  without  waste,  yields  a  definite  quantity 
of  heat ;  and,  conversely,  this  heat,  if  there  be  no  waste,  can  per- 
form the  original  quantity  of  mechanical  work. 

165.  Transformation,    Correlation,    and    Conservation    of 
Energy.     The  proof  of  the  facts  just  stated  was  one  of  the 
most  important  steps  in  the  establishment  of  the  grand  twin 
conceptions  of  modern  science  :  (1)  that  all  kinds  of  energy  are 
so  related  to  one  another  that  energy  of  any  kind  can  be  trans- 
formed into  energy  of  any  other  kind,  —  known  as  the  doctrine 


160 


MOLECULAR    DYNAMICS. 


of   CORRELATION    OF    ENERGY  ;    (2)    that   when   one  form  of 
energy  disappears,  its  exact  equivalent  in  another  form  always 
takes  its  place,  so  that  the  sum  total  of  energy  is  unchanged)  — 
known  as  the  doctrine  of  CONSERVATION  OF  ENERGY. 

These  two  doctrines  are  admirably  summarized  by  Maxwell 
as  follows  :  "  The  total  energy  of  any  body  or  system  of  bodies  is 
a  quantity  which  can  neither  be  increased  nor  diminished  by 
any  mutual  action  of  these  bodies,  though  it  may  be  transformed 
into  any  of  the  forms  of  which  energy  is  susceptible."  Since 
all  bodies  of  matter  in  the  universe  constitute  a  system,  it 


FIG. 128. 

follows  from  the  above  that  the  sum  total  of  energy  in  the 
universe  is  a  constant  quantity.  Neither  creation  nor  annihi- 
lation of  energy  is  possible  through  any  agency  known  to 
man.  These  doctrines  constitute  the  corner  stones  of  modern 
physical  science.  Chemistry  teaches  that  there  is  a  conser- 
vation of  matter,  i.e.  that  matter  is  neither  creatable  nor 
annihilable  through  any  known  natural  agency  or  process. 

166.  Joule's  Experiment.  The  experiment  to  ascertain  the 
"  mechanical  value  of  heat,"  as  performed  by  Dr.  Joule  of 
England,  was  conducted  about  as  follows  : 


MECHANICAL   EQUIVALENT   OF   HEAT.  161 

A  copper  vessel,  B  (Fig.  128),  was  provided  with,  a  paddle 
wheel  (indicated  by  the  dotted  lines)  which  rotated  about  a 
vertical  axle,  A.  The  axle  was  rotated  by  the  weights  E  and 
F,  the  cord  of  each  being  so  arranged  that  each  weight,  in 
falling,  rotated  the  axle  in  the  same  direction.  By  turning 
the  crank  above  A  the  weights  are  raised  to  any  desired  hight 
measured  on  the  scales  G  and  H. 

The  resistance  offered  by  the  water  to  the  motion  of  the 
paddles  was  the  means  by  which  the  mechanical  energy  of 
the  weights  was  converted  into  heat,  which  raised  the  tem- 
perature of  the  water.  Taking  two  bodies  whose  combined 
mass  was,  e.g.,  80  k.,  he  raised  them  a  measured  distance,  e.g. 
53  m.  high  ;  by  so  doing  4240  kgm.  of  work  were  performed 
upon  them,  and  consequently  an  equivalent  amount  of  energy 
was  stored  up  in  them,  ready  to  be  converted,  first  into  that 
of  mechanical  motion,  then  into  heat.  He  took  a  definite 
mass  of  water  to  be  agitated,  e.g.  2k.,  at  a  temperature  of 
0°  C.  After  the  descent  of  the  weights,  the  water  was  found 
to  have  a  temperature  of  5°  C.  ;  consequently  the  2  k.  of  water 
must  have  received  10  calories  of  heat  (careful  allowance 
being  made  for  all  losses  of  heat),  which  is  the  number  of 
calories  that  is  equivalent  to  4240  kgm.  of  mechanical  energy  ; 
or  one  calorie  is  equivalent  to  4%4  kgm.  of  mechanical  energy. 

In  other  words,  to  produce  a  quantity  of  heat  required  to 
raise  1  kilogram  of  water  through  1°  (7.,  4® 4  kilogrammeters  of 
mechanical  energy  must  be  consumed.  What  the  experiment 
really  shows  is  that  whenever  a  certain  quantity  of  mechanical 
energy  is  converted  into  heat,  the  number  of  thermal  units 
produced  is  always  proportional  to  the  mechanical  energy 
consumed,  or  to  the  work  done. 

167.  Mechanical  Equivalent  of  Heat.  As  a  converse  of  the 
above  it  may  be  demonstrated  by  actual  experiment  that  the 
quantity  of  heat  required  to  raise  1  k.  of  water  from  0°  to 
1°  C.  will,  if  converted  into  work,  raise  a  424  k.  weight  1  m. 


162 


MOLECULAR    DYNAMICS. 


high,  or  1  k.  weight  424  m.  high.  In  terms  of  the  British 
system,  the  same  fact  is  stated  as  follows  :  The  quantity  of 
heat  that  will  raise  the  temperature  of  1  pound  of  water  from 
60°  to  61°  F.  wiU  raise  772.55  pounds  1  foot  high.  The 
quantity,  424  kgm.,  is  called  the  mechanical  equivalent  of  one 
calorie,  or  Joule's  equivalent.  Or  we  may  say  that  one  calorie 
is  the  thermal  equivalent  of  424  kgm.  of  work. 


SECTION  XIII. 
THERMODYNAMICS    CONTINUED.  —  STEAM   ENGINE. 

168.  Description  of  a  Steam  Engine.  A  steam  engine  is  a 
machine  in  which  the  elastic  force  of  steam  is  the  motive 
agent.  Inasmuch  as  the  elastic  force  of  steam  is  entirely  due 
to  heat,  the  steam  engine  is  properly  a.  heat  engine  ;  that  is,  it 


FIG.  129. 


is  a  machine  by  means  of  which  heat  is  continuously  trans- 
formed into  work,  or  the  energy  of  mass  motion.  The 
modern  steam  engine  consists  essentially  of  an  arrangement 
by  which  steam  from  a  boiler  is  conducted  to  each  side 


DESCRIPTION    OF    A    STEAM   ENGINE.  163 

of  a  piston  alternately  ;  and  then,  having  done  its  work  in 
driving  the  piston  to  and  fro,  is  discharged  from  each  side 
alternately,  either  into  the  air  or  into  a  condenser. 

The  diagram  in  Fig.  129  will  serve  to  illustrate  the  general  features 
and  the  operation  of  a  steam  engine.  The  details  of  the  various  mechani- 
cal contrivances  are  purposely  omitted,  so  as  to  present  the  engine  as 
nearly  as  possible  in  its  simplicity. 

In  the  diagram,  A  represents  the  steam  pipe  through  which  steam 
passes  from  the  boiler  to  a  small  chamber,  D,  called  the  valve-chest.  In 
this  chamber  is  a  slide-valve,  G,  which,  as  it  is  moved  to  and  fro,  opens 
and  closes  alternately  the  passages  leading  from  the  valve-chest  to  the 
cylinder  B,  and  thus  admits  the  steam  alternately  each  side  of  the  piston  C. 
When  one  of  these  passages  is  open,  the  other  is  always  closed. 

In  the  position  of  the  valve  represented  in  the  diagram,  the  passage  F 
is  open,  and  steam  entering  the  cylinder  at  the  bottom  drives  the  piston 
upward.  At  the  same  time  the  steam  on  the  upper  side  of  the  piston 
escapes  through  the  passage  E  and  the  exhaust-port  H.  While  the  pis- 
ton rises,  the  valve  closes  the  passage  F  leading  from  the  valve-chest  and 
opens  the  passage  E  into  the  same,  and  thus  the  order  of  things  is 
reversed. 

Motion  is  communicated  by  the  piston  through  the  piston  rod  K  and 
the  walking  beam  L  L  to  the  crank  M,  and  by  this  means  the  shaft  carry- 
ing a  fly-wheel,  N  N,  is  rotated.  Connected  with  an  eccentric  on  the 
shaft  is  the  rod  o  o,  which  by  a  simple  device  communicates  a  to-and-fro 
motion  to  the  slide-valve  G.  Motion  is  also  communicated  by  the  band 
e  e  'to  the  governor  d,  which  is  caused  to  rotate.  If  the  speed  of  the  parts, 
due  to  undue  pressure  of  steam,  become  excessive,  the  centrifugal  tend- 
ency will  cause  the  arms  of  the  governor  to  rise  and  thereby  close  the 
throttle-valve  b  and  thus  shut  off  steam. 

The  fly-wheel  is  a  large,  heavy  wheel,  having  the  larger  portion  of  its 
mass  located  near  its  circumference  ;  it  serves  as  a  reservoir  of  energy, 
which  is  needed  to  make  the  rotation  of  the  shaft  and  all  other  machin- 
ery connected  with  it  uniform,  so  that  sudden  changes  of  velocity 
resulting  from  sudden  changes  of  the  driving  power  or  resistances  may 
be  avoided. 

When  the  exhaust  steam  escapes  through  H  into  the  air 
the  engine  is  said  to  be  a  high-pressure  or  a  non-condensing 
engine  ;  when  it  is  led  to  a  condensing  chamber  (as  J  in  the 


164  MOLECULAR    DYNAMICS. 

figure)  and  there  condensed  by  a  spray  of  cold  water  for  the 
purpose  of  reducing  the  back  pressure  of  the  atmosphere,  the 
engine  is  called  a  low-pressure  or  a  condensing  engine. 

This  water  must  be  pumped  out  of  the  condenser  by  a  special  pump,  R, 
called  technically  the  air-pump ;  thus  a  partial  vacuum  is  maintained. 
The  advantage  of  such  an  engine  is  obvious,  for  if  the  exhaust-pipe, 
instead  of  opening  into  a  condenser,  communicate  with  the  outside  air, 
as  in  the  non-condensing  engine,  the  steam  is  obliged  to  move  the  piston 
constantly  against  a  resistance  arising  from  atmospheric  pressure  of  15 
pounds  for  every  square  inch  of  the  surface  of  the  piston.  But  in  the 
condensing  engine  a  large  portion  of  the  pressure  on  the  exhaust  side  of 
the  piston  is  removed  and  an  equivalent  portion  of  the  pressure  on  the 
steam  side  is  utilized  and  made  to  do  useful  work.  In  well-proportioned 
condensmg  apparatus  the  pressure  on  the  exhaust  side  may  be  reduced 
90  per  cent,  so  that  the  moving  piston  instead  of  working  against  a 
resistance  of  15  pounds  meets  with  a  resistance  of  only  1.5  pounds  per 
square  inch. 

169.  Steam  Gauge.    An  instrument  called  a  steam  gauge  is  con- 
nected with  the  boiler.     It  measures  the  excess  of  the  pressure  of  the 
steam  at  any  instant  above  the  atmospheric  pressure.     The  absolute 
pressure  of  the  steam  (i.e.  measured  from  zero)  is  the  pressure  indicated 
by  the  steam  gauge  plus  the  pressure  of  the  atmosphere  at  the  time. 

170.  Power  of  a  Steam  Engine.     The   horse-power   of    a 
steam  engine  is  calculated  by  means  of  the  following  formula  : 

(Mean  effective  pressure  in  pounds  per  square  inch  on 
piston  X  area  of  piston  in  square  inch  X  length  of  stroke  in 
feet  X  number  of  strokes  per  minute)  -f-  33,000. 

The  steam  engine,  with  all  its  merits  and  with  all  the 
improvements  which  modern  mechanical  art  has  devised,  is 
an  exceedingly  wasteful  machine.  The  best  engine  that  has 
been  constructed  utilizes  less  than  15  per  cent  of  the  heat 
energy  generated  by  the  combustion  of  the  fuel. 

EXERCISES. 

1.  Why  does  the  temperature  of  steam  suddenly  fall  as  it  moves  the 
piston  ? 

2.  What  do  you  understand  by  a  ten  horse-power  steam  engine  ? 


EXERCISES.  165 

3.  Upon  what  does  the  power  of  a  steam  engine  depend  ? 

4.  The  area  of  a  piston  is  500  square  inches,  and  the  average  unbal- 
anced steam  pressure  is  30  pounds  per  square  inch.     What  is  the  total 
effective  pressure  ?     Suppose  that  the  piston  travels  30  inches  at  each 
stroke,  and  makes  100  strokes  per  minute,  40  per  cent  being  allowed  for 
wasted  energy,  what  power  does  the  engine  furnish,  estimated  in  horse- 
powers ? 

5.  Can  ice  at  0°  C.,  and  under  ordinary  atmospheric  pressure,  have  its 
temperature  raised  ?    Explain. 

6.  Find  the  resulting  temperature  (C*.)  of  the  following  mixtures: 
(a)  5  k.  of  snow  at  0°  with  25  k.  of  water  at  28°. 

(6)  4  k.  of  ice  at  —  10°  with  30  k.  of  water  at  50°. 
(c)  10  k.  of  iron  at  200°  with  2  k.  of  ice  at  0°. 

7.  How  many  thermal  units  are  required  to  change  5  k.  of  ice  at 
-  10°  C.  into  water  at  10°  ? 

8.  If  30  g.  of  steam  at  100°  C.  be  passed  into  400  g.  of  ice-water  at 
0°  C.,  what  will  be  the  temperature  of  the  mixture  ? 

9.  A  building  is  heated  by  hot-water  pipes.     How  does  heat  get  from 
the  furnace  of  the  boiler  to  a  person  in  the  building  ? 

10.  A  building  is  heated  by  steam  pipes.     How  does  heat  get  from  the 
furnace  to  objects  in  the  building  ? 

11.  A  rod  of  copper  at  0°C.  measures  10  feet ;  its  length  at  100°  C. 
is  0.191  inch  greater.     Find  the  coefficient  of  expansion  of  copper. 

12.  A  silver  rod  at  0°  C.  is  10  feet  long.     Find  its  length  at  100°  C. 

13.  A  kettle  contains  2  k.  of  water  at  60°  C.     How  much  heat  must 
be  supplied  to  vaporize  all  the  water  ? 

14.  In  what  state  is  heat  when  it  is  not  manifest  to  the  senses  ? 

15.  Which  plays  the  greater  part  in  the  heating  of  a  room,  convection 
or  conduction  ? 

16.  Why  are  woolen  blankets  good  both  for  keeping  a  person  warm 
in  winter  and  for  preserving  ice  in  summer  ? 

17.  Explain  the  benefit  derived  from  double  windows  and  double 
doors  in  cold  climates. 

18.  At  what  temperature  will  a  liter  hold  the  greatest  quantity  of 
water  ? 

19.  Explain  how  a  piece  of  iron  hammered  on  an  anvil  becomes  hot. 

20.  What  temperature  of  the  arbitrary  Centigrade  scale  corresponds 
to  450°  of  the  absolute  scale  ? 

21.  (a)  Why  do  metals  and  marble  in  a  cold  room  feel  colder  than 
wood  and  flannel  ?     (6)  Why  do  the  latter  in  a  hot. oven  feel  cooler  than 
the  former  ? 


CHAPTER   V. 


ENERGY  OF  MASS  VIBRATION.  -  SOUND- 
WAVES. 


SECTION  I. 
STUDY   OF   VIBRATIONS   AND   WAVES. 

THE  subjects  of  Sound-waves  and  Light- waves,  which  we  are  about  to 
study,  have  two  important  characteristics  in  common  that  distinguish  them 
from  the  subjects  already  studied.  First,  each  of  them 
affects  its  peculiar  organ  of  sense,  the  ear  or  the  eye. 
Secondly,  both  originate  in  vibrating  bodies,  and  reach 
us  only  by  the  intervention  of  some  medium  capable  of 
being  set  in  vibration. 


FIG. 130. 


171.  Simple  Harmonic  Motion.  The  motion 
of  a  lead  bullet  (Fig.  130)  suspended  by  a 
A  thread  and  set  swinging  in  a  circular  path  in  a 
horizontal  plane  is  practically  uniform.  When 

viewed  from   above   its  path   appears 

circular,  when  viewed  obliquely  its  path 

appears  elliptical,  and  when  the  eye  is 

placed  on  the  same  level  with  it  the 

motion  appears  to  be  in  a  straight  line, 

M  N  (Fig.  131).     The  apparent  motion 

of  the  bullet,  when  viewed  from  this 

position,  is  the  projection  of  uniform 

circular    motion    on    a   straight    line. 

While  the  bullet  passes  points   1,2,3, 

etc.,   lines    drawn   from    these    points 

normal  to  the  line  M  N  intersect  it  in  points  !,  H,  C,  etc.    While 

the  bullet  moves  over  equal  spaces  1-2,  2-3,  etc.,  in  equal 


AL      K 


I      H  C 


FIG. 131. 


DIRECTION   OF   VIBRATION.  167 

intervals  of  time,  the  speed  of  the  point  of  intersection  is 
variable,  as  shown  by  the  unequal  spaces  I  H,  H  C,  etc.,  trav- 
ersed by  this  point  in  equal  intervals  of  time.  Such  a  motion 
as  that,  whether  in  a  line,  an  ellipse,  or  a  circle,  executed  in 
equal  intervals  of  time,  is  called  simple  harmonic  motion,  and 
it  is  the  kind  of  motion  with  which  we  have  to  deal  chiefly  in 
the  study  of  sound  and  light. 

It  is  the  kind  of  motion  executed  by  the  vibrating  prongs  of  a  tuning 
fork,  and,  generally,  by  the  vibrating  parts  of  all  musical  instruments.  It 
is  the  kind  of  motion  into  which  the  particles  of  air  are  thrown  when  the 
atmosphere  is  traversed  by  sound-waves,  and  that  is  set  up  in  the  ether 
(§211)  when  it  is  traversed  by  light- waves  or  electrical  waves. 

The  time  occupied  by  a  particle  in  executing  a  single  com- 
plete harmonic  motion,  i.e.  from  A  to  C  and  back,  is  called  the 
period  of  a  complete  vibration.  The  extent  of  the  vibration 
on  either  side  of  the  middle  point,  as  A  J  or  J  C,  is  called  the 
amplitude  of  the  vibration. 

172.  Direction  of  Vibration. 

Experiment  1.  Grasp  one  end  of  a  small  rod  or  yardstick  in  a  vise, 
pull  the  free  end  to  one  side,  and  set  it  in  vibration.  Pluck  a  string  of  a 
piano  or  violin.  Note  that  the  motions  of  all  the  bodies  which  thus  far 
we  have  caused  to  vibrate  are  at  right  angles  to  their  length.  These  are 
called  transverse  vibrations. 

Experiment  2.  Suspend  a  spiral  spring  or  an  elastic  cord  with  a 
small  weight  attached  at  the  lower  end  ;  lift  the  weight,  and,  dropping  it, 
notice  that  the  spring  or  cord  vibrates  lengthwise.  This  is  a  case  of 
longitudinal  vibration.  There  may  also  be  torsional  vibrations ;  for  exam- 
ple, children  often  amuse  themselves  by  producing  these  by  twisting  a 
curtain  cord  and  tassel. 

173.  Wave-motion.     Imagine  a  series  of  particles  moving 
with  harmonic  motion  in  parallel  straight  lines  A,  B,  C,  D,  etc. 
(Fig.  132),  so  that  each  succeeding  particle  begins  to  move  a 
definite   time  later   than  the   preceding  one.     Suppose,  for 
example,  that  the  period  of  vibration  is  one  second,  and  that 
each  particle  begins  to  move  -fa  of  a  second  later  than  the 


168 


MOLAR    DYNAMICS. 


preceding  one.  Draw  a  circle  whose  radius  represents  the 
amplitude  of  vibration,  and  divide  it  into  twelve  equal  parts. 
Let  the  particle  in  line  A  be  at  a  (i.e.  at  4  in  the  circle)  ;  then 
the  particle  in  line  B  will  be  T^  of  a  period  behind,  that  is, 
at  b  j  the  particle  in  C  will  be  at  c,  etc.  Join  points  a,  b,  c, 
etc.,  and  a  curve  (represented  by  the  thick  line)  is  formed.  In 
T\  second  the  particle  in  A  will  have  moved  from  a  to  a'  (in  the 
circle  from  4  to  7);  b  will  have  moved  to  b',  etc.  Join  these 


ABCDEFGH    I    JKLMNOPQRS 


I 


\ 


\ 


\i 


FIG.  132. 

points,  and  the  dotted  curve  a',  b',  c',  d',  etc.,  will  be  formed. 
The  crest  has  moved  from  E  to  H  ;  the  wave-form  is  moving 
from  A  toward  S.  In  |f  second,  or  one  period,  the  particles 
will  be  in  their  original  positions,  but  the  crest  of  the  wave 
will  have  moved  from  E  to  Q.  This  distance,  or  the  distance 
from  any  particle  to  the  next  particle  that  is  in  a  similar  posi- 
tion in  its  path  and  is  moving  in  the  same  direction  (e.g.  b  to 
n,  c  to  o)  is  called  a  wave-length.  The  wave-length  may  also 
be  denned  as  the  distance  the  wave  travels  in  one  period. 

Since  the  wave  travels  one  wave-length  in  a  period,  to 
determine  the  velocity  with  which  the  wave  travels,  it  is 
only  necessary  to  determine  the  number  of  wave-lengths  the 
wave  passes  over  in  a  period  of  time.  Thus, 

v  =  I  X  n, 

in  which  v,  I,  and  n  represent,  respectively,  velocity,  wave- 
length, and  number  of  wave-lengths. 


VIBRATIONS. 


169 


174.  Graphical  Method  of  Studying  Vibrations. 


Experiment  1.     Attach,  by  means  of  sealing-wax,  a  bristle  or  a  fine 
wire  to  the  end  of  one  of  the  prongs  of  a  large  steel  fork  (like  a  tuning 
fork,  but  larger)   called  a 
diapason.     Set  the  fork  in 
vibration,  and  quickly  draw 
the  point  of  the  bristle  lightly  FIG.  133. 

over  smoked  glass  (A,  Fig.  133).  A  beautiful  wavy  line  will  be  traced 
on  the  glass,  each  wave  corresponding  to  a  vibration  of  the  prong  when 
vibrating  as  a  whole. 

Next,  tap  the  fork,  near  its  stem,  on  the  edge  of  a  table,  and  trace  its 
vibrations  on  a  smoked  glass  as  before.  You  will  generate  a  similar 
set  of  waves,  but  running  over  these  is  another  set,  of  much  shorter 


3VWV\AAAAAAAAAAAAAAAAAAAAAAAAA/WVWWVWWWWWVWWW\ 


Fig.  134. 

period,  like  the  lower  line  of  Fig.  134,  showing  that  the  prong  vibrates, 
not  only  as  a  whole,  but  in  parts.  The  serrated  wavy  line  produced  rep- 
resents the  resultant  of  the  combined  vibrations,  and  may  be  called  a 
complex  wave-line. 

The  vibration  frequency  of  a  fork  may  easily  be  found  by  means  of 
an  apparatus  called  a  vibrograph.     One  of  the  tines  of  the  fork  a  (Fig. 

135)  has  a  small  elastic  indicator 
attached  to  its  extremity.  The 
sharp  point  of  this  indicator 
touches  a  smoked  glass  plate,  k, 
below.  Above  the  glass  plate  is 
suspended  a  pendulum  with  a 
heavy  bob.  Beneath  the  bob  is 

^-^^       *  another    indicator   which    just 

T[TI^  grazes  the  glass  as  it  passes  the 

lower  part  of  its  arc.  The  ex- 
perimenter first  finds  the  exact  fraction  of  a  second  occupied  by  the 
pendulum  in  making  one  complete  or  double  vibration.  The  fork  is 


170  MOLAR   DYNAMICS. 

then  put  in  vibration  and  the  block  h,  carrying  the  glass  plate,  is  drawn 
along  beneath  the  style,  which  marks  upon  the  glass  a  wave-line.  At 
the  same  time  the  pendulum  is  set  swinging  and  allowed  to  traverse  the 
plate  width-wise  three  times,  making,  with  its  indicator,  three  lines 
athwart  the  wave-line.  Now  the  interval  of  time  between  the  instants 
when  the  first  and  the  third  of  these  lines  are  made  is  the  period  of  one 
complete  vibration.  The  number  of  vibrations  which  the  fork  made  in 
this  interval  may  be  determined  from  the  sinuous  curved  line  intervening 
between  the  lines  made  by  the  pendulum.  The  number  of  vibrations 
made  by  the  fork  in  a  certain  fraction  of  a  second  having  been  ascer- 
tained in  this  manner,  the  vibration  number  per  second  is  calculated 
therefrom. 

175.  How  Vibratory  Motion,  i,e.  a  Wave,  is  Propagated 
through  an  Elastic  Medium. 

Experiment  2.  Fig.  136  represents  a  spring  brass  wire  wound  into 
the  form  of  a  spiral,  about  12  feet  long.  Attach  one  end  to  a  cigar  box, 
and  fasten  the  box  to  a  table.  Hold  the  other  end  of  the  spiral  firmly  in 

c 


FIG.  136. 

one  hand,  and  with  the  other  hand  insert  a  knife  blade  between  the  turns 
of  the  wire,  and  quickly  rake  it  for  a  short  distance  along  the  spiral 
toward  the  box,  thereby  crowding  closer  together  for  a  little  distance  ( B) 
the  turns  of  wire  in  front  of  the  hand,  and  leaving  the  turns  behind 
pulled  wider  apart  (A)  for  about  an  equal  distance.  The  crowded  part 
of  the  spiral  may  be  called  a  condensation,  and  the  stretched  part  a  rare- 
faction. The  condensation,  followed  by  the  rarefaction,  runs  with  great 
velocity  through  the  spiral,  strikes  the  box,  producing  a  sharp  thump  ; 
is  reflected  from  the  box  to  the  hand,  and  from  the  hand  again  to  the  box, 
producing  a  second  thump  ;  and  by  skillful  manipulation  three  or  four 
thumps  will  be  produced  in  rapid  succession.  If  a  piece  of  twine  be  tied 
to  some  turn  of  the  wire,  it  will  be  seen,  as  each  wave  passes  it,  to  receive 
a  slight  jerking  movement  forward  and  backward  in  the  direction  of  the 
length  of  the  spiral. 

The  effect  of  applying  force  with  the  hand  to  the  spiral 
spring  is  to  produce  in  a  certain  section,   B,  of  the  spiral  a 


FLUIDS    AS    MEDIA    OF    WAVE-MOTION.  171 

crowding  together  of  the  turns  of  wire,  and  at  A  a  separation  ; 
but  the  elasticity  of  the  spiral  instantly  causes  B  to  expand, 
the  effect  of  which  is  to  produce  a  crowding  together  of  the 
turns  of  wire  in  front  of  it,  in  the  section  C,  and  thus  a  for- 
ward movement  of  the  condensation  is  made.  At  the  same 
time,  the  expansion  of  B  causes  a  filling  up  of  the  rarefaction 
at  A,  so  that  this  section  is  restored  to  its  normal  state.  This 
is  not  all;  the  folds  in  the  section  B  do  not  stop  in  their 
swing  when  they  have  recovered  their  original  position,  but, 
like  a  pendulum,  swing  beyond  the  position  of  rest,  thus 
producing  a  rarefaction  at  B,  where  immediately  before  there 
was  a  condensation.  Thus  a  forward  movement  of  the  rare- 
faction is  made,  and  thus  a  pulse  or  wave  is  transmitted 
with  uniform  velocity  through  a  spiral  spring  or  any  elastic 
medium. 

A  wave  cannot  be  transmitted  through  an  inelastic  soft 
brass  spiral.  Elasticity  is  essential  in  a  medium,  in  order  that 
it  may  transmit  waves  composed  of  condensations  and  rarefac- 
tions ;  and  the  greater  the  elasticity  in  a  medium,  the  greater 
the  facility  and  rapidity  with  which  it  transmits  waves. 

176.  Fluids  as  Media  of  Wave-motion. 

Experiment  3.     Arrange  apparatus  as  shown  in  Fig.  137.     The  whole 
is  filled  with  water,  except  the  glass  bulb  A, 
and  a  portion  of  the  glass  tube  connected  with      '''^ 
it.     Glass  tubes  C  and  D  are  connected  by  a 
rubber  tube,  E,  10  or  12  feet  long.     The  top  of 
the  thistle  tube  N  is  covered  with  thin  sheet 
rubber. 

Tap  with  the  end  of  a  finger  the  diaphragm 
N  ;  the  water  column  in  S  is  instantaneously 
thrown  into  oscillations.  The  observer  should 
note  the  promptness  with  which  the  water  in  S 
responds  to  any  impulse  given  the  diaphragm. 

The  impulse  is  transmitted  by  wave-motion  with  a  velocity  of  about 
1435  meters  (4708  feet)  per  second. 

Experiment  4.  Place  a  candle  flame  at  the  orifice  a  of  the  long  tin 
tube  A  (Fig.  138),  and  strike  the  table  a  sliarp  blow  with  a  book  near  the 


172  MOL^R   DYNAMICS. 

orifice  b.     Instantly  the  candle  flame  is  quenched.     The  body  of  air  in 
the  tube  serves  as  a  medium  for  transmission  of  motion  to  the  candle. 


FIG.  138. 

Is  the  motion  transferred  that  of  a  current  of  air  through  the  tube  (a 
miniature  wind),  or  is  it  a  vibratory  motion  ?  Burn  touch-paper l  at  the 
orifice  b,  so  as  to  fill  this  end  of  the  tube  with  smoke,  and  repeat  the  last 
experiment. 

Evidently,  if  the  body  of  the  air  be  moved  along  through 
the  tube,  the  smoke  will  be  carried  along  with  it.  The  candle 
is  blown  out  as  before,  but  no  smoke  issues  from  the  orifice  a. 
It  is  clear  that  there  is  no  translation  of  material  particles 
from  one  end  to  the  other  —  nothing  like  the  flight  of  a  rifle 
bullet.  The  candle  flame  is  struck  by  something  like  a  pulse 
of  air,  not  by  a  wind.2 

Air  is  a  fluid,  and  therefore  has  only  volume  elasticity. 
The  only  waves  it  can  propagate  are  waves  composed  of  com- 
pressions and  rarefactions.  There  are  two  important  dis- 
tinctions between  these  waves  and  waves  of  water,  or  waves 
sent  along  a  cord  when  one  end  is  shaken  :  (1)  the  former 
consist  of  condensations  and  rarefactions ;  the  latter  of  ele- 
vations and  depressions  ;  (2)  in  the  former  the  vibrations  of 
the  particles  are  in  the  same  line  with  the  path  of  the  wave, 

1  To  prepare  touch-paper,  dissolve  about  a  teaspoonful  of  saltpeter  in  a  half-tea- 
cupful  of  hot  water,  dip  unsized  paper  in  the  solution,  and  then  allow  it  to  dry.    The 
paper  produces  much  smoke  in  burning,  but  no  flame. 

2  If  a  membrane  be  tied  tightly  over  the  orifice  b  and  a  sudden  blow  be  given  it 
(e.g.  by  snapping  it  with  a  finger),  the  vibratory  character  of  the  motion  communi- 
cated through  the  tube  is  well  shown  by  the  fact  that  the  flame  is  first  driven  from  the 
orifice  a  and  immediately  afterward  drawn  toward  it. 


SOUND    AND    SOUND-WAVES.  173 

and  hence  they  are  called  longitudinal  vibrations  ;  in  the  latter 
the  vibrations  take  place  in  planes  at  some  angle  to  the  path 
of  the  wave,  and  are  therefore  called  transverse  vibrations. 
As  an  air-wave  advances,  every  individual  particle  concerned 
in  its  transmission  performs  a  short  excursion  to  and  fro  in 
the  direction  of  a  straight  line  radiating  from  the  source  of 
the  waves. 


SECTION  II. 
SOUND   AND    SOUND-WAVES. 

177.  Sound  and  Sound-waves  Defined.      Sound  is  a  sensation 
caused  usually  by  air-ivaves  beating  upon  the  organ  of  hearing.1 

Sound-ivaves  are  waves  in  any  medium  (usually  air)  that  are 
capable  of  producing  the  sensation  of  sound. 

If  we  could  see  the  air  as  it  is  traversed  by  sound-waves, 
we  should  see  spherical  shells  of  condensed  air  alternating 
with  shells  of  rarefied  air.  The  condensed  portions  corre- 
spond to  localities  of  greater  pressure,  while  the  rarefied 
portions  represent  localities  of  smaller  pressure.  When  there 
is  an  increase  of  pressure  on  the  drumhead  of  the  ear  it  is 
pushed  in,  and  when  the  pressure  becomes  less  the  drumhead 
springs  back  to  its  former  position. 

178.  Sound-waves  Originate  in  Mass-vibration.  A  body  vibrat- 
ing in  an  elastic  medium,  e.g.  in  air,  does  not  necessarily  produce  sound- 
waves ;   in  other  words,  not  all  waves  are  sound-waves.     For  example, 
the  energy  of  the  vibrations  may  be  insufficient,  or  the  vibrating  body 
may  be  so  small  (or  the  medium  so  rare)  that  it  cuts  through  the  medium 
without  condensing  it  sufficiently  to  produce  audible  effects. 

1  As  commonly  used,  the  term  sound  is  ambiguous,  being  applied  to  both  a  sensation 
and  the  physical  cause  of  the  sensation.  With  sound  as  a  sensation  we  have  little  to 
do,  as  this  is  a  physiological  rather  than  a  physical  phenomenon.  No  more  appro- 
priate name  than  sound-wave  can  be  applied  to  the  physical  agent  with  which  we 
are  to  deal ;  it  suggests  at  once  the  reality,  and  is  not  suggestive  of  some  vague 
mysterious  thing  shot  through  space.  Sound  is  a  condition,  not  a  thing. 


174  MOLAR   DYNAMICS. 

Experiment  1.  Strike  a  bell  or  a  glass  bell-jar,  and  touch  the  edge 
with  a  small  ivory  ball  suspended  by  a  thread ;  you  not  only  hear  the 
sound,  but,  at  the  same  time,  you  see  a  tremulous  motion  of  the  ball, 
caused  by  a  motion  of  the  bell.  Touch  the  bell  gently  with  a  finger,  and 
you  feel  a  tremulous  motion.  Press  the  hand  against  the  bell ;  you  stop 
its  vibratory  motion,  and  at  that  instant  the  sound  ceases.  Watch  the 
strings  of  a  piano,  guitar,  or  violin,  or  the  tongue  of  a  jew's-harp,  when 
sounding.  You  can  see  that  they  are  in  motion. 

As  a  bell  while  sounding  possesses  no  peculiar  property 
except  motion,  it  has  nothing  to  communicate  but  motion. 
The  vibrations  of  a  sonorous  body  cannot  be  communicated 
to  the  ear  unless  there  be  a  continuous  intervening  medium 
of  some  kind. 

Experiment  2.  Lay  a  thick  tuft  of  cotton  wool  on  the  plate  of  an 
air-pump,  and  on  this,  face  downward,  place  a  loud-ticking  watch,  and 
cover  with  the  receiver.  Notice  that  the  receiver,  interposed  between 
the  watch  and  your  ear,  greatly  diminishes  the  sound,  or  interferes  with 
the  passage  of  something  to  the  ear.  Partially  exhaust  the  air  by  a  few 
strokes  of  the  pump,  and  listen  ;  the  sound  is  more  feeble,  and  continues 
to  grow  less  and  less  distinct  as  the  exhaustion  progresses,  until  either 
no  sound  can  be  heard  when  the  ear  is  placed  close  to  the  receiver,  or  an 
extremely  faint  one,  as  if  coming  from  a  great  distance.  The  removal 
of  air  from  a  portion  of  the  space  between  the  watch  and  your  ear  pre 
vents  the  passage  of  sound-waves  to  your  ear.  Let  in  the  air  again,  and 
the  sound  is  again  heard. 

179.  Solids  and  Liquids  are  Capable  of  Transmitting  Sound- 
waves. 

Experiment  3.  Place  one  end  of  a  long  pole  on  a  cigar  box,  and 
apply  the  stem  of  a  vibrating  tuning  fork  to  the  other  end  ;  the  sound- 
vibrations  will  be  transmitted  through  the  pole  to  the  box,  and  a  sound 
will  be  given  out  by  the  box,  as  though  that,  and  not  the  tuning  fork, 
were  the  origin  of  the  sound. 

Experiment  4.  Place  the  ear  to  the  earth,  and  listen  to  the  rumbling 
of  a  distant  carriage  ;  or  put  the  ear  to  one  end  of  a  long  stick  of  timber, 
and  let  some  one  gently  scratch  the  other  end  with  a  pin. 


VELOCITY   OF    SOUND-WAVES.  175 

SECTION  III. 
VELOCITY   OF   SOUND-WAVES. 

180.  Velocity  of  Sound-waves  Dependent  on  Elasticity  and 
Density  of  Medium.  The  velocity  with  which  a  particle  of  an 
elastic  medium  vibrates,  and  therefore  the  velocity  of  propa- 
gation in  the  medium  (i.e.  the  velocity  of  a  sound-wave),  is 
directly  proportional  to  the  square  root  of  the  elasticity  of  the 
medium,  and  inversely  proportional  to  the  square  root  of  its 
density.  The  relation  of  these  quantities  is  shown  in  the 
formula 


Too  ^/-. 

If  the  elasticity  and  density  of  the  medium  vary  alike,  and 
in  the  same  direction,  it  is  evident  that  the  velocity  of  the 
sound-wave  is  unaffected.  Hence  the  velocity  of  a  sound- 
wave is  unaffected  by  barometric  hight,  or  elevation  above 
sea  level.  Temperature,  however,  affects  only  the  density  of 
air.  Elevation  of  temperature  of  the  air  diminishes  the  den- 
sity of  the  air,  and  therefore  tends  to  increase  the  speed  of 
the  sound-wave.  The  velocity  of  a  sound-wave  is  greatest  in 
the  direction  of  the  wind.  Velocity  of  sound-waves  is  very 
nearly  independent  of  pitch  and  intensity. 

The  greater  density  of  solids  and  liquids,  as  compared  with 
gases,  tends,  of  course,  to  dimmish  the  velocity  of  sound-waves; 
but  their  greater  incompressibility  more  than  compensates 
for  the  decrease  of  velocity  occasioned  by  the  increase  of  den- 
sity. As  a  general  rule,  solids  are  more  incompressible  than 
liquids  ;  hence  sound-waves  generally  travel  faster  in  the 
former  than  in  the  latter.  For  example,  sound-waves  travel 
in  water  about  four  times  as  fast  as  in  air,  arid  in  iron  and 
glass  sixteen  times  as  fast. 

The  velocity  of  sound-waves  in  air  at  0°  C.  is  332.4  m. 
(nearly  1091  feet)  per  second.  The  increase  of  velocity  per 
degree  C.  is  .608  m.  (23.9  inches)  per  second. 


176  MOLAR   DYNAMICS. 

SECTION  IV. 
ENERGY    OF    SOUND-WAVES.      LOUDNESS. 

181.  Energy  of  Sound-waves  Depends  on  the  Amplitude  of 
Vibration. 

Fix  your  attention  upon  a  particle  of  air  as  a  sound-wave 
passes  it.  At  a  certain  point  of  its  vibratory  excursion  its 
velocity  is  at  its  maximum.  Now  since  the  energy  of  a  mov- 
ing particle  varies  as  the  square  of  its  velocity,  the  intensity 
of  the  impact  which  it  is  capable  of  producing  upon  the  ear 
is  proportional  to  the  square  of  this  maximum  velocity. 

It  is  also  clear  that  if  the  amplitude  of  vibration  of  a 
particle  be  doubled  while  its  period  remains  constant,  its 
velocity  is  doubled,  and  therefore  its  energy  is  increased  four- 
fold. Hence,  (1)  measured  mechanically,  the  energy  of  a 
sound-wave  is  proportional  to  the  square  of  the  amplitude  of 
the  vibration  of  particles,  or,  it  is  proportional  to  the  square  of 
the  maximum  velocity  of  the  vibrating  particles. 

Loudness  of  sound  refers  to  the  intensity  of  %a  sensation. 
We  have  jio  standard  of  measurement  for  a  sensation,  so  we 
are  compelled  to  measure  the  energy  of  the  sound-wave, 
knowing  at.the  same  time  that  loudness  is  not  proportional  to 
this  energy. 

182.  Energy  of  Sound-waves  Depends  upon  the  Density  of 
the  Medium.     In  the  experiment  with  the  watch  under  the 
receiver  of  the  air-pump  (p.  174),  the  sound  grew  feebler  as 
the  air  became  rarer.     Aeronauts  are  obliged  to  exert  them- 
selves more  to   make  their   conversation  heard  when  they 
reach  great  hights  than  when  in  the  denser  lower  air.     In 
diving-bells  persons  are  obliged  to  speak  in  undertones.     In  a 
rare  medium,  either  a  vibrating  body  sets  in  motion  fewer 
particles  during  a  single  vibration,  as  in  the  case  of  the  par- 
tially exhausted  receiver,  or,  as  in  the  case  of  the  hydrogen 


SPEAKING-TUBES.  177 

gas,  it  sets  in  motion  particles  of  less  mass  than  in  a  dense 
medium  ;  consequently  it  parts  with  its  energy  more  slowly, 
and  the  sound  is  weaker. 

(2)  The  energy  of  gaseous  sound-waves  increases  with  the 
density  of  the  medium  in  which  they  are  produced. 

183.  Energy  of  Sound-waves  Depends  on  Distance  from  their 
Source.     It   is  a  matter  of   everyday  observation   that  the 
loudness  of  a  sound  diminishes  very  rapidly  as  the  distance 
from  the  source  of  the  waves  to  the  ear  increases.     As  a 
sound-wave  advances  in  an  ever-widening  sphere,  a  given 
quantity  of  energy  becomes  distributed  over  an  ever-increasing 
surface  ;  and  as  a  greater  number  of  particles  partake  of  the 
motion,  the  individual  particles  receive  proportionately  less 
energy ;  hence  it  follows,  —  as  a  consequence  of  the  geomet- 
rical truth  that  "  the  surface  of  a  sphere  varies  as  the  square 
of  its  radius/7  —  that  (3)  the  energy  of  a  sound-wave  varies 
inversely  as  the  square  of  the  distance  from  the  source.     This  is 
known  as  the  Law  of  Inverse  Squares. 

184.  Speaking-tubes. 

Experiment.  Place  a  watch  at  one  end  of  the  long  tin  tube  (Fig.  138), 
and  the  ear  at  the  other  end.  The  ticking  sounds  very  loud,  as  though 
the  watch  were  close  to  the  ear. 

Long  tin  tubes,  called  speaking-tubes,  passing  through  many 
apartments  in  a  building,  enable  persons  at  the  distant  ex- 
tremities to  carry  on  conversation  in  a  low  tone  of  voice, 
while  persons  in  the  various  rooms  through  which  the  tube 
passes  hear  little  or  nothing.  The  reason  is  that  the  sound- 
waves which  enter  the  tube  are  prevented  from  expanding, 
consequently  the  energy  of  the  sound-waves  is  not  affected  by 
distance,  except  as  it  is  wasted  by  friction  of  the  air  against 
the  sides  of  the  tube,  and  by  internal  friction  due  to  the 
viscosity  of  the  air. 


178 


MOLAR   DYNAMICS. 


SECTION  V. 

CHANGES    IN    DIRECTION    OF    PROPAGATION    OF    SOUND- 
WAVES. 

185.  Reflection.  So  long  as  sound-waves  are  not  obstructed 
in  their  motion  they  are  propagated  in  the  form  of  concentric 
spheres ;  but  when  they  meet  with  an  obstacle,  they  follow 
the  general  law  of  elastic  bodies ;  that  is,  they  return  upon 
themselves,  forming  new  concentric  waves,  called  reflected 
waves,  which  seem  to  emanate  from  a  second  center  on  the 
other  side  of  the  reflecting  body.  This  phenomenon  is  called 
the  reflection  of  sound-waves. 

A  (Fig.  139)  represents  a  vibrating  particle  or  a  sonorous  center  from 
which  emanates  a  series  of  waves.  P  Q  represents  an  obstacle  with  a  flat 
surface  turned  toward  the  waves.  Take,  for  example,  the  incident  wave 
M  C  D  N,  emitted  from  the  center  A  ;  the  corresponding  reflected  wave  is 
represented  by  the  arc  C  K  D  of  a  circle  whose  center  a  is  as  far  beyond 
the  obstacle  P  Q  as  A  is  in  front  of  it. 


Join  any  point,  C,  of  the  reflecting  surface  to  the  sonorous  center,  and 
the  line  A  C  represents  one  of  an  infinite  number  of  directions  in  which 
energy  is  transmitted  by  a  sound-wave.  Such  a  line  may  conveniently  be 
called  a  sound-ray.  Let  fall  the  line  H  C  normal  to  the  surface  at  the 


SOUND-WAVES    REFLECTED    BY    MIRRORS.  179 

point  of  incidence  C.  The  angle  AC  H_is.calle(i-tJbLe_fluif/ie  of  incidence. 
The  ray  A  C  after  reflection  takes  the  direction  C  B,  which  is  a  prolon- 
gation of  a  C.  The  angle  B  C  H  is  called  the  angle  of  reflection.  An 
observer  at  B  receives  sound-waves  not  only  directly  from  A  in  the  line 
A  B,  but  also  from  C  in  the  line  C  B.  Hence  he  hears  two  sounds,  one 
(to  speak  in  common  parlance)  proceeding  from  point  A,  and  the  other 
from  point  C.  The  latter  travels  from  A  to  C  and  from  C  to  B,  a  longer 
distance  than  A  B,  and  is  therefore  heard  later  than  the  former.  If  the 
interval  of  time  between  their  arrivals  at  B  be  greater  than  about  a  fifth  of 
a  second,  the  ear  is  able  to  separate  the  two  sensations  and  the  latter 
appears  as  an  echo.  If  the  interval  of  time  be  too  short,  then  only  a 
single  and  perhaps  somewhat  blurred  and  indistinct  sound  is  heard.  The 
latter  phenomenon  is  usually  called  resonance.  Such  an  effect  is  expe- 
rienced frequently  when  a  person  speaks  irfa  large  hall. 

If  the  obstacle  PQ  present  a  concave  surface,  the  wave-front  after 
reflection  will  be  less  convex,  arid  may  become  plane  or  even  concave, 
according  to  the  degree  of  the  concavity  of  the  reflector  and  the  position 
of  the  sounding  body. 

186.  Sound-waves  Reflected  by  Concave  Mirrors. 

Experiment.  Place  a  watch  at  the  focus  A  (Fig.  140)  of  a  concave 
mirror,  G.  At  the  focus  B  of 
another  concave  mirror,  H, 
place  the  large  opening  of  a 
small  tunnel,  and  with  a  rub- 
ber  connector  attach  the  bent 
glass  tube  C  to  the  nose  of 
the  tunnel.  The  extremity  D 
being  placed  in  th£  ear,  the  FIG 

ticking  of  the  watch  can  be 
heard  very  distinctly,  as  though  it  were  somewhere  near  the  mirror  H. 
Though  the  mirrors  be  many  feet  apart,  the  sound  will  be  louder  at  B 
than  at  an  intermediate  point  E. 

How  is  this  explained  ?  Every  air  particle  in  a  certain 
radial  line,  «as  Ac,  receives  and  transmits  motion  in  the 
direction  of  this  line  ;  the  last  particle  strikes  the  mirror 
at  c,  and,  being  elastic,  bounds  off  in  the  direction  cc',  com- 
municating its  motion  to  the  particles  in  this  line.  At  cf  a 
similar  reflection  gives  motion  to  the  air  particles  in  the  line 


180  MOLAR   DYNAMICS. 

cf  B.  In  consequence  of  these  two  reflections,  all  divergent 
sound-rays,  as  A  d,  A  e,  etc.,  that  meet  the  mirror  G  are  there 
rendered  parallel,  and  afterwards  rendered  convergent  at  the 
mirror  H.  The  practical  result  of  the  concentration  of  this 
scattering  energy  is  that  a  sound  of  great  intensity  is  heard 
at  B.  The  points  A  and  B  are  called  the  foci  of  the  mirrors. 
The  front  of  the  wave  as  it  leaves  A  is  convex,  in  passing  from 
G  to  H  it  is  plane,  and  from  H  to  B  it  is  concave.  If  you  fill  a 
large  circular  tin  basin  with  water,  and  strike  one  edge  with 
a  knuckle,  circular  waves  with  concave  fronts  will  close  in 
on  the  center,  heaping  up  the  water  at  that  point. 

Long  u  whispering  galleries"  have  been  constructed  on  this  principle. 
Persons  stationed  at  the  foci  of  the  concave  ends  of  the  long  gallery  can 
carry  on  a  conversation  in  a  whisper  which  persons  between  cannot  hear. 
The  external  ear  is  a  wave-condenser.  The  hand  held  concave  behind 
the  ear,  by  increasing  the  reflecting  surface,  adds  to  its  efficiency. 

SECTION  VI. 

REENFORCEMENT  OF    SOUND-WAVES  ;    INTERFERENCE    OF 
SOUND-WAVES. 

187.  Reenforcement  of  Sound-waves. 

Experiment  1.  Set  a  diapason  in  vibration ;  unless  it  is  held  near 
the  ear,  you  can  scarcely  hear  the  sound.  Press  the  stem  against  a  table  ; 
the  sound  rings  out  loud,  but  the  waves  seem  to  proceed  from  the  table. 

When  only  the  fork  vibrates,  the  prongs,  presenting  little 
surface,  cut  their  way  through  the  air,  producing  very  slight 
condensations,  and  consequently  waves  of  little  intensity. 
When  the  fork  rests  upon  the  table,  the  vibrations  are  com- 
municated to  the  table  ;  the  table  with  its  larger  surface 
throws  a  larger  mass  of  air  into  vibration,  and  thus  greatly 
intensifies  the  sound-waves.  The  strings  of  the  piano,  guitar, 
and  violin  owe  as  much  of  their  loudness  of  sound  to  their 
elastic  sounding-boards  as  the  fork  does  to  the  table. 


KESONATOltS. 


181 


188.  Beenforcement  by  Bodies  of  Air;  Resonators, 

Experiment  2.  Take  a  glass  tube,  A  (Fig.  141),  16  inches  long  and  2 
inches  in  diameter ;  thrust  one  end  into  a  vessel  of  water,  C,  and  hold 
over  the  other  end  a  vibrating  diapason,  B,  that  makes  (say)  256  vibra- 
tions in  a  second.  Gradually  lower  the  tube  into  the  water,  and  when  it 
reaches  a  certain  depth,  i.e.  when  the  column  of  air  oc  attains  a  certain 
length,  the  sound  becomes  very  loud ;  as  the  tube  is  lowered  below  this 
point,  the  sound  rapidly  dies  away. 

Columns  of  air,  as  well  as  sounding-boards,  serve  to  reenforce 
sound-waves.  The  instruments  which  enclose  the  columns 
of  air  are  called  resonators. 
Unlike  sounding-boards  they 
can  respond  loudly  to  only 
one  tone,  or  to  a  few  tones  of 
widely  different  pitch. 

How  is  this  reenforcement 
effected  ?  When  the  prong 
a  moves  from  one  extremity 
of  its  arc  a'  to  the  other  a", 
it  sends  a  condensation  down 
the  tube  ;  this  condensation, 
striking  the  surface  of  the 
water,  is  reflected  by  it  up  the 
tube.  Now  suppose  that  the  front  of  this  reflected  conden- 
sation should  just  reach  the  prong  at  the  instant  it  is  starting 
on  its  retreat  from  a"  to  a' ;  then  the  reflected  condensation 
will  combine  with  the  condensation  formed  by  the  prong  in 
its  retreat  to  make  a  greater  condensation  in  the  air  outside 
the  tube.  Again,  the  retreat  of  the  prong  from  a"  to  a' 
produces  in  its  rear  a  rarefaction,  which  also  runs  down  the 
tube,  is  reflected,  and  reaches  the  prong  at  the  instant  it  is 
about  to  return  from  a'  to  a",  and  to  cause  a  rarefaction  in  its 
rear  ;  these  two  rarefactions  moving  in  the  same  direction 
conspire  to  produce  an  intensified  rarefaction.  The  original 
sound-waves  thus  combine  with  the  reflected,  to  produce 


FIG.  141. 


182 


MOLAR    DYNAMICS. 


resonance  ;  but  this  can  happen  only  when  the  like  parts  of 
each  wave  coincide  each  with  each;  for  if  the  tube  were 
somewhat  longer  or  shorter  than  it  is,  it  is  plain  that  conden- 
sations and  rarefactions  would  meet  in  the  tube  and  tend  to 
destroy  each  other. 

The  loudness  of  sound  of  all  wind  instruments  is  due  to  the  resonance 
of  the  air  contained  within  them.  A  simple  vibratory  movement  at  the 
mouth  or  orifice  of  the  instrument,  scarcely  audible  in  itself  (such  as  the 
vibration  of  a  reed  in  reed  pipes,  or  a  pulsatory  movement  of  the  air, 
produced  by  the  passage  of  a  thin  sheet  of  air  over  a  sharp  wooden  or 
metallic  edge,  as  in  organ  pipes,  flutes,  and  flageolets,  or  more  simply  still 
by  the  friction  of  a  gentle  stream  of  breath  from  the  lips,  sent  obliquely 
across  the  open  end  of  a  closed  tube),  is  sufficient  to  throw  the  large 
body  of  air  enclosed  in  the  instrument  into  vibration,  and  the  sound  thus 
reenforced  becomes  audible  at  long  distances. 

Experiment  3.  Attach  a  rose  gas-burner,  A  (Fig.  142),  to  a  metal 
gas-pipe  about  1  m.  in  length,  and  connect  this  by  a  rubber  tube  with  a 
gas-nipple.  Light  the  gas  at  the  rose  burner,  and  you 
will  hear  a  low  rustling  noise.  Remove  the  conical  cap 
from  the  long  tin  tube  (Fig.  138),  support  the  tube  in  a 
vertical  position,  and  gradually  raise  the  burner  into  the 
tube  ;  when  it  reaches  a  certain  point  not  far  up,  the 
body  of  air  in  the  tube  will  catch  up  the  vibrations,  and 
give  out  deafening  sound-waves  that  will  shake  the  walls 
and  furniture  in  the  room. 

189.  Measuring  Wave-lengths  and  the  Speed 
of  Sound-waves.  Experiments  like  that  described 
on  p.  181  enable  us  readily  to  measure  the  length 
of  the  wave  produced  by  a  fork  whose  vibration 
number  is  known,  and  also  to  measure  the 
velocity  of  sound-waves.  It  is  evident  that  if  a 
condensation  generated  by  the  prong  of  the  fork 
in  its  forward  movement  from  a'  to  a"  (Fig.  141) 
meet  with  no  obstacle,  its  front,  meantime,  will  traverse  the 
distance  o  d,  or  twice  the  distance  o  c  ;  hence  the  length  of 
the  condensation  is  the  distance  o  d.  But  a  condensation  i§ 


FIG. 142. 


INTERFERENCE    OF    SOUND-WAVES. 


183 


only  one  half  of  a  wave,  and  the  passage  of  the  prong  from  a' 
to  a"  is  only  one  half  of  a  vibration  ;  consequently  the  distance 
o  d  is  one  half  of  a  wave-length,  and  the  distance  o  c  is  one 
fourth  of  a  wave-length.  The  measured  distance  of  o  c  in  this 
case  is  about  13.13  inches  ;  hence,  the  length  of  wave  pro- 
duced by  a  C'-fork  making  256  vibrations  in  a  second  is  about 
(13.13  inches  X  4  =  )  52.5  inches  =  4.38  feet.  And  since  a 
wave  from  this  fork  travels  4.38  feet  in  ^^  of  a  second,  it 
will  travel  in  an  entire  second  (4.38  feet  X  256  =)  1121  feet. 
The  distance  o  c  varies  with  the  temperature  of  the  air. 

It  is  evident  that  the  three  quantities  expressed  in  the 
formula 

velocity 


wave-length  = 


number  of  vibrations 


bear  such  a  relation  to  one  another  that  if  any  two  be  known, 
the  remaining  quantity  can  be  computed.  It  will  further  be 
observed  that  with  a  given  velocity  the  wave-length  varies 
inversely,  as  the  number  of 
vibrations;  i.e.  the  greater 
the  number  of  vibrations 
per  second,  the  shorter  the 
wave-length. 

190,    Interference    of 
Sound-waves. 

Experiment  4.  Hold  a  vibrat- 
ing diapason  over  a  resonance 
jar,  as  in  Fig.  143.  Roll  the 
diapason  over  slowly  in  the  fin- 
gers. At  certain  points  a  quarter 
of  a  revolution  apart,  when  the  diapason  is  in  an  oblique  position 
with  reference  to  the  edge  -of  the  jar  as  represented  in  the  figure, 
the  reenforcement  from  the  tube  almost  entirely  disappears,  but  it  reap- 
pears at  the  intermediate  points.  That  is,  there  are  four  intervals  in  the 
space  around  the  fork  where  the  two  series  of  waves  generated  by  the 
two  tines  interfere  to  produce  mutual  destruction,  These  are  called  tech- 


FIG.  143. 


184 


MOLAR   DYNAMICS. 


nically  the  cones  of  silence.  Return  to  the  position  where  there  is  no 
resonance,  and,  without  touching  the  diapason,  enclose  in  a  loose  roll  of 
paper  the  prong  farthest  from  the  tube,  so  as  to  prevent  the  sound-waves 
produced  by  that  prong  from  passing  into  the  tube  ;  the  resonance  result- 
ing from  the  vibrations  of  the  other  prong  immediately  appears. 

Two  sound-waves  may  combine  to  produce  a  sound  louder  or  weaker 
than  either  alone  would  produce,  or  may  even  cause  silence.  This  combina- 
tion of  sound-waves  to  produce  a  louder  or  weaker  sound  is  called 
interference. 

191.  Forced  and  Sympathetic  Vibrations. 

Experiment  5.  Suspend  from  a  frame  several  pendulums,  A,  B,  C, 
etc.  (Fig.  144).  A  and  D  are  each  3  feet  long, 
C  is  a  little  longer,  and  B  and  E  are  shorter. 
Set  A  in  vibration ;  slight  impulses  will  be 
communicated  through  the  frame  to  D,  and 
cause  it  to  vibrate.  The  vibration-period  of 
D  being  the  same  as  that  of  A,  all  the  impulses 
tend  to  accumulate  motion  in  D,  so  that  it  soon 
vibrates  through  arcs  as  large  as  those  of  A. 
On  the  other  hand,  C,  B,  and  E,  having  different 
rates  of  vibration  from  that  of  A,  will  at  first 
acquire  a  slight  motion,  but  soon  their  vibra- 
tions will  be  in  opposition  to  those  of  A,  and 
then  the  impulses  received  from  A  will  tend  to 


c 
JIG.  144. 


destroy  the  slight  motion  they  had  previously  acquired. 

Experiment  6.  Press  down  gently  one  of  the  keys  of  a  piano  so  as  to 
raise  the  damper  without  making  any  sound,  and  then  sing  loudly  into 
the  instrument  the  corresponding  note.  The  string  corresponding  to  this 
note  will  be  thrown  into  vibrations  that  can  be  heard  for  several  seconds 
after  the  voice  ceases.  If  another  note  be  sung,  this  string  will  respond 
only  feebly. 

Raise  the  dampers  from  all  the  strings  of  the  piano  by  pressing  the 
foot  on  the  right-hand  pedal,  and  sing  strongly  some  note  into  the  piano. 
Although  all  the  strings  are  free  to  vibrate,  only  those  will  respond  loudly 
that  correspond  to  the  note  you  sing,  i.e.  those  that  are  capable  of  making 
the  same  number  of  vibrations  per  second  as  are  produced  by  your  voice. 

So  the  pulses  or  waves  that  traverse  the  air  between  the 
vocal  organs  and  the  strings,  so  gentle  that  only  the  sensitive 
organ  of  the  ear  can  perceive  them,  become  great  enough  to 


PITCH    OF    MUSICAL    SOUNDS.  185 

bend  the  rigid  steel  wires  when  the  energy  of  their  blows, 
dealt  at  the  rate  of  perhaps  512  in  a  second,  accumulates. 
The  large  number  of  blows  makes  up  for  the  feebleness  of 
the  individual  blows. 

These  experiments  show  that  a  vibrating  body  tends  to 
make  other  bodies  near  it  vibrate,  even  if  their  periods  of 
vibrations  be  different.  Vibrations  of  this  kind,  such,  for 
example,  as  those  of  B,  C,  and  E,  in  Experiment  5,  and  those  gen- 
erated in  the  sounding-board  of  pianos,  violins,  etc.,  are  called 
forced  vibrations.  But  if  the  period  of  the  incident  waves  of 
air  be  the  same  as  that  of  the  body  which  they  cause  to 
vibrate,  the  amplitude  and  the  intensity  of  the  vibrations 
become  very  great,  like  that  of  the  pendulum  D,  and  those  of 
the  piano  strings  which  gave  forth  the  loud  sounds.  Such 
are  called  sympathetic  vibrations. 


SUCTION   VII. 
PITCH   OF   MUSICAL   SOUNDS. 

192.  On  what  Pitch  Depends. 

Experiment  1.  Draw  the  finger-nail  or  a  card  across  the  teeth  of  a 
oomb,  first  slowly  and  then  rapidly.  The  two  sounds  produced  are  com- 
monly described  as  low  or  grave,  and  high  or  acute.  The  hight  of  a 
musical  sound  is  its  pitch. 

Experiment  2.  Cause  the  circular  sheet-iron  disk  A  (Fig.  145)  to 
rotate,  and  hold  a  corner  of  a  visiting  card  so  that  at  each  hole  an  audible 
tap  shall  be  made.  Notice  that  when  the  separate  taps  or  noises  cease  to 
be  distinguishable,  the  sound  becomes  musical ;  also,  that  the  pitch  of 
the  musical  sound  depends  upon  the  rapidity  of  the  rotation,  i.e.  upon 
the  frequency  of  the  taps. 

Experiment  3.  Hold  the  orifice  of  a  tube,  B,  so  as  to  blow  through 
the  holes  as  they  pass.  When  the  rotation  is  slow,  separate  puffs,  from 
which  it  hardly  seems  possible  to  construct  a  musical  sound,  are  heard. 
When,  however,  the  ear  is  no  longer  able  to  detect  the  separate  puffs,  the 
sound  becomes  quite  musical,  and  the  pitch  rises  and  falls  with  the 
speed. 


186 


MOLAR    DYNAMICS. 


Pitch  depends  upon  the  number  of  sound-waves  striking  the 
ear  per  second,  or  upon  wave-length  y  i.e.  the  greater  the  number 
of  vibrations  per  second,  or  the  shorter  the  wave-length,  the  higher 
the  pitch. 

193.  Distinction  between  Noise  and  Musical  Sound.     If  the 

body  that  strikes  the  air  deal  it  but  a  single  blow,  like  the 

discharge  of  a  firecracker,  the  ear 
receives  but  a  single  shock,  and  the 
result  is  called  a  noise.  If  several 
shocks  be  slowly  received  by  the 
ear  in  succession,  the  ear  distin- 
guishes them  as  so  many  separate 
noises.  If,  however,  the  body  that 
strikes  the  air  be  in  vibration,  and 
deal  it  a  great  number  of  little 
blows  in  a  second,  or  if  a  large 
number  of  firecrackers  be  dis- 
charged one  after  another  very 
rapidly,  so  that  the  ear  is  unable  to 
distinguish  the  individual  shocks, 
the  effect  produced  is  that  of  one 
continuous  sound,  whicji  may  be 
pleasing  to  the  ear ;  and,  if  so,  it 
Continuity  alone  does  not  neces- 
sarily render  a  sound  musical.  There  must  exist  also  regu- 
larity both  in  the  periodicity  and  the  intensity  of  the  impulses. 
The  distinction  between  music  and  noise  is  a  distinction 
between  the  agreeable  and  the  disagreeable,  between  regularity 
and  confusion. 

194.  Musical  Scale.      Suppose  a  body,  e.g.  a  tuning  fork, 
to  make  261  vibrations  per  second,  the  sound  produced  is 


FIG.  145. 


is  called  a  musical  sound. 


recognized  by  our  musical  sense  as  the  note  jfc = —  which 


MUSICAL   SCALE.  187 

corresponds  with  the  so-called  middle  C  (c',  or  French  uts)  of 
a  piano  tuned  to  the  national  standard  pitch.1 

The  pitch  of  a  sound  produced  by  twice  as  many  vibrations 
as  that  of  another  sound  is  called  the  octave  of  the  latter. 
Between  two  such  sounds  the  voice  rises  or  falls,  in  a  manner 
very  pleasing  to  the  ear,  by  a  definite  number  of  steps  called 
musical  intervals.  This  gives  rise  to  the  so-called  diatonic 
scale,  or  gamut. 

The  number  of  vibrations  which  shall  constitute  a  given 
note  is  purely  arbitrary,  and  differs  slightly  in  different 
countries;  but  the  ratios  between  the  vibration  numbers  of 
the  several  notes  of  the  gamut  and  the  vibration  number  of 
the  first  or  fundamental  note  of  the  gamut  are  the  same 
among  all  enlightened  nations. 

The  successive  tones  of  the  diatonic  scale  of  C  are  related 
to  one  another  with  respect  to  vibration  frequency  as  follows  : 


•T^  — 

-s*5  

BE 

-G>- 

—  -&  — 

«£? 

?*?            ^^  — 

—  —  J 

c' 

d' 

e' 

i'             g/ 

ax 

b' 

c/x 

No.  of  vi- 

Ut3 

re3 

mi3 

fa3         so!3 

Ia3 

Si3 

Ut4 

brations. 

261 

293.62 

326.25 

348        391.5 

435 

489.37 

522 

Ratios 

256 

:    288     : 

320    : 

341.3    :    384     : 

426 

:    480     : 

512 

or 

1 

9 
~S 

f       : 

I        :      f       : 

| 

:      V       = 

2 

The  ear  is  wholly  incapable  of  determining  the  number  of 
vibrations  corresponding  to  a  given  tone,  but  it  is  capable  of 
determining  with  wondrous  precision  the  ratio  of  the  vibration 
numbers  of  two  notes  ;  hence  all  music  must  depend  upon  the 
recognition  of  such  ratios,  and  for  this  reason  the  vibration 
ratios  given  above  are  of  the  utmost  importance.  An  octave 
below  c'  is  c  ;  two  octaves  below,  c1?  and  so  on.  In  a  similar 
manner  the  octaves  below  any  other  tone  are  indicated. 

1  In  a  convention  of  piano  manufacturers  held  in  New  York,  it  was  decided  that 
the  national  pitch,  to  go  into  effect  July  1,  1892,  should  be  the  standard  French, 
Austrian,  and  Italian  pitch  of  435  (A$)  double  vibrations  in  a  second  at  68°  F. 


188  MOLAR    DYNAMICS. 


EXERCISES. 

1.  Find  the  vibration  number  for  each  note  of  the  scale  of  which  c"  is 
the  first  note. 

2.  What  is  the  vibration  number  of  c  an  octave  below  c'  ? 

3.  Find  the  wave-length  corresponding  to  each  note  of  the  scale  of 
which  c'  is  the  first,  when  the  temperature  of  the  air  is  10°  C. 

4.  Find  the  length  of  a  resonance  tube   (disregarding  its  diameter) 
closed  at  one  end,  which  will  respond  to  c"  when  the  temperature  is 
16°  C. 

5.  The  same  singer  may  not  be  able  to  sing  twice  alike,  i.e.  in  the 
same  key.     How  is  it  possible  that  the  singing  in  both  instances  may  be 
equally  correct  ? 

6.  Why  does  the  same  bell  always  give  a  sound  of  nearly  the  same 
pitch  ? 

7.  (a)  What  is  the  effect  of  striking  a  bell  with  different  degrees  of 
force  ?     (b)   What  change  in  the  vibrations  is  produced  ?     (c)   What 
property  of  the  sound  remains  the  same  ? 

8.  (a)  Strike  a  key  of  a  piano  and  hold  it  down.     What  is  the  only 
change  you  observe  in  the  sound  produced,  while  it  remains  audible  ? 
(b)  What  is  the  cause  of  this  change  ? 

SECTION    VIII. 

COMPOSITION   OF    SONOROUS    VIBRATIONS  AND  THEIR 
RESULTANT   WAVE-FORMS. 

195.  Coexistence  and  Superposition  of  Waves.  —  Interfer- 
ence. When  two  or  more  currents  of  waves  traverse  the  same 
medium  at  the  same  time  and  in  the  same  or  opposite  direc- 
tions, so  that  one  set  of  waves  is,  as  it  were,  superposed  upon 
another,  all  the  vibratory  motions  peculiar  to  the  several  waves 
are  imparted  to  every  particle  of  the  medium  simultaneously. 
When  two  or  more  systems  of  waves  act  on  a  particle  at  the 
same  time,  they  are  said  to  interfere.  The  resultant  motion 
of  any  particle  at  a  given  instant  may  be  found  on  the  prin- 
ciple of  parallelogram  of  motions  ;  or,  in  case  the  several 
motions  are  parallel  and  occur  at  the  same  time,  the  resultant 
is  the  algebraic  sum  of  the  several  motions. 


SONOROUS    VIBRATIONS. 


189 


This  will  be  best  understood  by  means  of  graphical  representations. 
In  A  (Fig.  146)  the  wave-lines  of  two  coexisting  currents  of  waves  having 
the  same  wave-length  and  phase, 
while  the  amplitude  of  one  is 
greater  than  that  of  the  other, 
are  represented  by  dotted  lines. 
For  example,  the  amplitudes  of 
the  vibrations  for  the  particle  a  are, 
respectively,  a  c  and  a  e.  Their 
algebraic  sum  is  a d.  In  like  man- 
ner the  displacement  of  any  par- 
ticle of  the  medium  traversed  by 
the  several  wave-currents  at  any 
instant  is  determined.  The  heavy 
line  represents  the  form  of  the 
joint  wave  resulting  from  the 
combination  of  the  two.  It  will  be  seen  that  the  only  change  is  one  of 
amplitude  or  intensity. 

In  B  are  two  wave-currents  whose  waves  are  of  the  same  length  and 
amplitude,  but  have  a  difference  of  phase  of  £  of  a  period  ;  i.e.  one  is  a 


B 


FIG.  146. 


FIG.  147. 

quarter  of  a  wave-length  behind  the  other.     The  result  is  a  wave  of  the 
same  length  but  of  different  phase  and  amplitude. 

In  A  (Fig.  147)  are  given  two  wave-currents  whose  wave-lengths  are  as 
1  :  £  and  whose  phases  in  the  beginning  agree.     The  resultant  of  this 


190 


MOLAR*  DYNAMICS. 


combination  with  still  another  of  f  the  wave-length  of  the  longest  is 
shown  in  B.  In  C  is  the  same  combination  as  in  A,  but  the  phases  differ 
by  J  of  a  period  of  the  shorter  wave. 

In  the  diagrams  given  above  only  transverse  vibrations  are  represented, 
but  the  results  there  depicted  apply  equally  well  to  longitudinal  vibrations 
and  to  waves  of  condensations  and  rarefactions.  In  Fig.  148  the  heavy 


FIG. 148. 

line  A  B  is  a  typical  representation  of  the  resultant  of  two  currents  of 
aerial  sound-waves  an  octave  apart,  while  the  rectangular  diagram  C  D 
is  intended  to  represent  a  portion  of  a  transverse  section  of  a  body  of 
air  traversed  by  the  joint  wave  corresponding  to  the  heavy  wave-line 
above.  The  depth  of  shading  in  different  parts  indicates  the  degree  of 
condensation  or  rarefaction  at  those  parts. 


SECTION  IX. 

VIBRATION   OF    STRINGS. 

196.  Sonometer.     This  instrument  consists  of  two  or  more 
piano  wires  of  different  thicknesses  stretched  lengthwise  over 

C 


FIG.  149. 


a  resonance  box.  One  end  of  each  wire  is  attached  to  the 
shorter  arm  of  a  bent  lever,  A  or  B  (Fig.  149),  and  the  tension 
of  the  wire  is  regulated  both  by  the  lengths  of  the  longer 


STATIONARY   VIBRATIONS.  191 

arms  employed  and  by  the  magnitude  of  the  weights  suspended 
therefrom.  The  length  of  the  vibrating  portion  of  the  strings 
is  regulated  by  the  sliding  bridge  C. 

Experiment  1.  Remove  the  bridge  C,  pluck  one  of  the  strings  with 
the  fingers  at  the  middle  point,  causing  it  to  vibrate  as  a  whole,  and  note 
the  pitch  of  the  sound.  Place  the  bridge  under  the  same  wire,  and  move 
it  gradually  toward  one  end  of  the  sonometer,  thereby  shortening  the 
vibrating  portion  ;  the  pitch  rises  as  the  vibrating  portion  is  shortened. 
Vary  the  position  of  C  until  a  pitch  is  obtained  an  octave  above  the  pitch 
given  at  first  when  the  entire  wire  was  vibrating.  It  will  be  found  that 
the  length  of  the  wire  which  gives  the  higher  note  is  just  half  the  original 
length  ;  i.e.  by  halving  the  wire  its  vibration-number  is  doubled.  At  two 
thirds  its  original  length,  it  gives  a  note  at  an  interval  of  a  fifth  above 
that  given  by  its  original  length ;  and  generally  the  reciprocals  of  the 
fractions  (§  194)  representing  the  relative  vibration-numbers  of  the  several 
notes  of  a  scale  represent  the  relative  lengths  of  the  wires  that  produce  these 
notes. 

Now  increase  the  tension  of  the  wire  ;  the  pitch  rises.  Increase  the 
tension  until  the  pitch  has  risen  an  octave ;  it  will  be  found  that  the 
tension  has  been  increased  fourfold. 

Next  try  two  wires  whose  lengths  and  tension  are  the  same,  but  whose 
diameters  are  (say)  as  1  :  2,  and  whose  masses  per  unit  length  are  conse- 
quently as  1  :  4  ;  the  pitch  given  by  the  wire  of  greater  mass  is  an  octave 
lower  than  the  pitch  given  by  the  other  wire. 

These  conclusions  may  be  summarized  thus  :  The  vibration- 
numbers  of  strings  of  the  same  material  vary  inversely  as  their 
lengths  and  the  square  roots  of  their  masses  per  unit  length,  and 
directly  as  the  square  roots  of  their  tensions. 

197.  Stationary  Vibrations,  Nodes,  etc. 

Experiment  2.  Hold  one  end  of  a  rubber  tube  about  2  m.  long,  while 
the  other  is  fixed,  and  send  along  it  a  regular  succession  of  equal  pulses 
from  the  vibrating 

hand.      By    varying     ^  e  ^---"    '/::";i]ni^Tr>>>^b  ^-""" 
the  tension  a  little,  it 
will  be  easy  to  obtain 
a  succession  of  gauzy 

spindles  (Fig.  150)  separated  by  points  that  are  nearly  or  quite  at  rest. 
Unlike  the  earlier  experiments,  the  waves  here  do  not  appear  to  travel 


192 


MOLAR    DYNAMICS. 


along  the  tube ;  yet  in  reality  they  do  traverse  it.  The  deception  is 
caused  by  stationary  points  being  produced  by  the  interference  of  the 
advancing  and  retreating  waves. 

This  interference  of  direct  and  reflected  waves  gives  rise 
to  an  important  class  of  phenomena  called  stationary  vibra- 
tions. The  points  of  least  motion,  as  a,  b,  and  e  (Fig.  150),  are 
called  nodes  (from  fancied  resemblance  to  knots)  ;  the  points 
of  greatest  amplitude,  as  d  and  c,  are  called  antinodes;  and  the 
portions  between  the  nodes  are  called  venters. 

In  a  similar  manner  a  string  may  be  made  to  vibrate  in  3, 
4,  etc.,  parts,  as  shown  in  C,  D,  and  E  (Fig.  151).  The  pitch 


FIG.  151. 

of  the  tone  produced  by  a  string  when  it  vibrates  as  a  whole, 
as  in  A,  is  called  the  fundamental  pitch  of  the  string.  The 
vibration  frequency  when  the  string  divides  into  halves,  as 
in  B,  is  twice  as  great  as  before,  and  consequently  the  pitch  of 
the  tone  produced  is  an  octave  above  that  of  the  fundamental. 
Generally  the  vibration  frequency  varies  as  the  number  of 
venters  into  which  the  string  divides. 

Tones  produced  by  a  string  or  other  body  when  it  vibrates 
in  parts  are  called  overtones  or  partial  tones.  If  the  overtones 
harmonize  (§  201)  with  the  fundamental  of  the  vibrating 
body,  they  are  called  harmonics. 

198.  Complex  Vibrations. 

Experiment  3.  Press  down  the  C'-key  of  a  piano  gently,  so  that  it 
will  not  sound,  and  while  holding  it  down,  strike  the  C-key  strongly. 
In  a  few  seconds  release  the  latter  key,  so  that  its  damper  will  stop  the 


TONES    AND    NOTES.  193 

vibrations  of  the  string  that  was  struck,  and  you  will  hear  a  sound  which 
you  will  recognize  by  its  pitch  as  coming  from  the  C'-wire.  Place  your 
finger  lightly  on  the  C'-wire,  and  you  will  find  that  it  is  indeed  vibrating. 
Press  down  the  right  pedal  with  the  foot,  so  as  to  lift  the  dampers  from 
all  the  wires,  strike  the  C-key,  and  touch  with  the  finger  the  C'-wire  ; 
it  vibrates.  Touch  the  wires  next  to  C',  viz.  B  and  D' ;  they  have  only 
a  slight  forced  vibration.  Touch  G' ;  it  vibrates. 

It  is  evident  that  the  vibrations  of  the  C'  and  Gr  wires 
are  sympathetic.  Now,  a  C-wire  vibrating  as  a  whole  cannot 
cause  sympathetic  vibrations  in  a  C-wire  ;  but  if  it  vibrates 
in  halves,  it  may.  Hence,  we  conclude  that  when  the  C-wire 
was  struck  it  vibrated,  not  only  as  a  whole,  giving  a  sound  of 
its  own  pitch,  but  also  in  halves  ;  and  the  result  of  this  latter 
set  of  vibrations  was  that  an  additional  sound  was  produced 
by  this  wire,  just  an  octave  higher  than  the  first-mentioned 
sound. 

Agaittj  the  G'-wire  makes  391.5  vibrations  in  a  second,  or 
three  times  as  many  (130.5)  as  are  made  by  the  C-wire  :  hence, 
the  latter  wire,  in  addition  to  its  vibrations  as  a  whole  and  in 
halvei^TOust  have  vibrated  in  thirds,  inasmuch  as  it  caused 
the  G'-wire  to  vibrate.  It  thus  appears  that  a  string  may 
vibrate  at  the  same  time,  as  a  whole,  in  halves,  thirds,  etc., 
and  the  result  is  that  a  sensation  is  produced  that  is  com- 
pounded of  the  sensations  of  several  sounds  of  different  pitch. 
A  sound  so  simple  that  it  cannot  be  resolved  is  called  a  tone. 

199,  Tones  and  Notes.  A  sound  composed  of  many  tones 
is  called  a  note. 

Not  only  do  stringed  instruments  produce  notes,  but  no 
ordinary  musical  instrument  is  capable  of  producing  a  simple 
tone,  i.e.  a  sound  generated  by  vibrations  of  a  single  period. 
In  other  words,  when  any  note  of  any  musical  instrument  is 
sounded^  there  is  produced,  in  addition  to  the  primary  tone,  a 
number  of  other  tones  in  a  progressive  series,  each  tone  of  the 
series  being  usually  of  less  intensity  than  the  preceding.  The 


194  MOLAR    DYNAMICS. 

primary  or  lowest  tone  of  a  note  is  usually  sufficiently  intense 
to  be  the  most  prominent,  and  hence  is  called  the  fundamental 
tone. 

Strings  when  struck  produce  many  overtones,  which  vary 
according  to  the  plaae  where  they  are  struck,  the  nature  of  the 
stroke,  and  the  density,  rigidity,  and  elasticity  of  the  string. 

200.  Beats. 

Experiment  4.  Strike  simultaneously  the  lowest  note  of  a  piano  and 
its  sharp  (black  key  next  above),  and  listen  to  the  resulting  sound. 

You  hear  a  peculiar  wavy  or  throbbing  sound,  caused  by  an 
alternate  rising  and  sinking  in  loudness.  Each  recurrence  of 
the  maximum  intensity  is  called  a  beat. 

Let  the  continuous  curved  line  AC  (Fig.  152)  represent  a 
series  of  waves  caused  by  striking  the  lo^^^ey,  and  the 

MM* 


FIG. 152. 

dotted  line  a  series  of  waves  proceeding  from  the  upper  key. 
Now,  the  waves  from  both  keys  may  start  together  at  A,  but 
as  the  waves  from  the  lower  key  are  given  less  frequently,  so 
are  they  correspondingly  longer,  and  at  certain  intervals,  as 
at  B,  condensations  will  correspond  with  rarefactions,  pro- 
ducing by  their  interference  momentary  silence,  too  short, 
however,  to  be  perceived  ;  but  the  sound  as  perceived  by  the 
ear  is  correctly  represented  in  its  varying  loudness  by  the 
curved  line  A'  B'  C'.  . 

It  will  be  apparent  from  the  study  of  Fig.  152  that  exactly 
one  beat  will  occur  in  each  interval  of  time  during  which  the 


ORIGIN    OF    DISCORD    AND    HARMONY.  195 

acuter  of  two  simple  tones  performs  one  more  vibration  than 
the  graver  tone. 

Hence,  the  number  of  beats  per  second  due  to  two  simple  tones 
is  equal  to  the  difference  of  their  respective  vibration-numbers. 

201.  Origin  of  Discord  and  Harmony.  Discord  produced 
by  two  sounds  is  explained  by  the  fact  that  the  sounds  produce 
beats,  which  do  not  coalesce  because  the  interval  between  them 
is  too  long. 

As  the  frequency  of  the  beats  increases,  a  point  is  finally 
reached  where  they  cease  to  be  recognized  as  distinct 
sounds,  and  where  they  blend  into  a  more  or  less  pure 
tone.  Beats  may  thus  coalesce  to  produce  beat-tones  that 
are  musical. 

It  must  not,  however,  be  inferred  that  dissonance  disap- 
pears immediately  upon  the  intermittences  becoming  too  rapid 
for  individual  recognition.  If  two  tones  form  a  narrower 
interval  than  a  minor  third,  the  combined  sound  is  harsh  and 
grating  on  the  ear. 

Two  tones  must  be  in  unison  to  produce  absolutely  perfect 
harmony.  The  intervals  that  most  nearly  approach  perfect 
harmony  are,  first,  that  of  the  octave,  and  secondly,  that  of 
the  fifth. 

That  two  notes  sounded  together  may  harmonize,  it  is  essential 
not  only  that  the  pitch  of  their  fundamental  tones  be  so  widely 
different  that  they  cannot  produce  audible  beats,  but  that  no 
audible  beats  shall  be  formed  by  their  overtones^  or  by  an  over- 
tone and  a  fundamental. 

Observe  that  the  relation  between  the  vibration-numbers  of 
the  fundamentals  of  C  and  C',  C  and  G,  C  and  F,  and  C  of 
any  diatonic  scale  and  any  note  in  the  same  scale,  can  be 
expressed  in  terms  of  small  numbers,  e.g.  1  :  2,  2  :  3,  3  :  4, 
etc.  (see  §  194).  Generally,  those  notes  and  only  those  har- 
monize whose  fundamental  tones  bear  to  one  another  ratios 
expressed  by  small  numbers  ;  and  the  smaller  the  numbers  which 


196  MOLAR    DYNAMICS. 

express  the  ratios  of  the  rates  of  vibration,  the  more  perfect  is 
the  harmony  of  two  sounds. 

Not  only  may  two  notes  whose  relative  vibration  frequency 
is  expressible  by  a  simple  ratio  harmonize,  but  three  or  four 
may  concur  with  the  same  result.  A  sound  produced  by  the 
coexistence  of  three  or  more  notes  is  called  in  music  a  chord. 
A  consonant  chord  is  a  concord  ;  a  dissonant  chord  is  a  discord. 


SECTION  X. 

QUALITY    OF    SOUND. 

202.  Complex  Sound-waves.  Simple  sound-waves  can  differ 
only  in  length  and  amplitude  ;  consequently  the  sounds  which 
they  produce  can  differ  only  in  pitch  and  loudness.  Complex 
sound-waves  may  differ,  as  we  have  seen,  in  form,  and  this 
gives  rise  to  a  property  of  sound  called  quality  (by  musicians, 
timbre).  Quality  is  that  property  of  sound,  not  due  to  pitch 
or  intensity,  that  enables  us  to  distinguish  one  sound  from 
another. 

Although  the  variety  of  sounds  one  hears  appears  well-nigh 
infinite,  yet  no  two  sounds  can  differ  from  each  other  in  any 
other  respect  than  pitch,  loudness,  or  quality.  The  length, 
amplitude,  and  form  of  the  wave  completely  determine  the 
wave,  and  these  three  elements  of  a  wave  are  mutually  inde- 
pendent, i.e.  any  one  may  be  changed  without  altering  the 
other  two.  Loudness  depends  on  amplitude  of  vibrations, 
pitch  on  vibration  frequency,  and  quality  on  complexity  of 
the  motion  of  the  vibrating  particles. 

Let  the  same  note  be  sounded  with  the  same  intensity, 
successively,  on  a  variety  of  musical  instruments,  e.g.  a  violin, 
cornet,  clarinet,  accordion,  jew's-harp,  etc.  ;  each  instrument 
will  send  to  your  ear  the  same  number  of  waves,  and  the 
waves  from  each  will  strike  the  ear  with  the  same  force,  yet 
the  ear  is  able  to  distinguish  a  decided  difference  between  the 


ANALYSIS    OF   MUSICAL    SOUNDS.  197 

sounds — a  difference  that  enables  us  instantly  to  identify 
the  instruments  from  which  they  come.  Sounds  from  instru- 
ments of  the  same  kind,  but  by  different  makers,  usually 
exhibit  decided  differences  of  character.  For  instance,  of  two 
pianos,  the  sound  of  one  will  be  described  as  richer  and  fuller, 
or  more  ringing,  or  more  "wiry,"  etc.,  than  the  other.  No 
two  human  voices  sound  exactly  alike. 

SECTION  XI. 

ANALYSIS   OF   SOUND-WAVES. 

203.  Analysis  of  Musical  Sounds.    Every  enclosed  body  of  air 
may  act  as  a  resonator  to  a  sound  of  suitable  wave-length.     A  seashell 
held  to  the  ear  "roars "  continually  in  response  to  the  outside  air,  which 
is  ever  disturbed  with  waves. 

By  means  of  a  set  of  resonators  corresponding  to  the  various  tones 
used  in  music,  it  is  possible  to  detect  the  component  tones  of  sounds 
which  are  far  too  complex  to  be  analyzed  by  the  unaided  ear.  Such  a 
resonator  (Fig.  153)  is  composed  of  two  brass 
cylinders,  one  telescoping  into  the  other,  the 
latter  being  drawn  out  conically  to  a  small  open 
tip,  A,  which  fits  the  ear.  The  length  is  thus 
adjustable,  and  the  resonator  will  respond, 
according  to  its  length,  to  any  single  tone. 

When  any  musical  sound  is  produced  near  the  orifice  C  of  one  of 
these  resonators,  and  suitable  adjustments  are  made,  the  ear  placed  at 
the  tip  A  is  able  to  single  out,  from  the  total  number  of  tones  composing 
the  note,  those  overtones  to  which  alone  this  resonator  is  capable  of 
responding.  By  applying  one  resonator  after  another  to  the  ear  a  sound 
is  analyzed  into  its  components.  It  is  thus  found,  for  instance,  that  the 
notes  of  a  clarinet  are  composed  only  of  the  odd  harmonics,  or  of  tones 
whose  vibration-numbers  are  in  the  ratios  of  1  :  3 :  5  :  7. 

204.  The  Phonautograph  or  Phonograph,    Sound-waves,  how- 
ever complex,  may  be  caused  permanently  to  record  the  succession  and 
variation  of  their  impulses,  and  thus,  as  it  were,  to  inscribe  their  own 
autograph.     Fig.  154  represents  the  original  Edison  phonograph. 

A  metallic  cylinder,  A,  is  rotated  by  means  of  a  crank.  On  the  surface 
of  the  cylinder  is  cut  a  shallow  helical  groove  running  around  the  cylinder 
from  end  to  end,  like  the  thread  of  a  screw.  A  small  metallic  point,  or 


198 


MOLAR    DYNAMICS. 


style,  projecting  from  the  under  side  of  a  thin  metallic  disk,  D  (Fig.  155), 
which  closes  one  orifice  of  the  mouthpiece  B,  stands  directly  over  the 
thread.  By  a  simple  device  the  cylinder,  when  the  crank  is  turned,  is 

made  to  advance  just  rapidly 
enough  to  allow  the  groove 
to  keep  constantly  under  the 
style.  The  cylinder  is  cov- 
ered with  tin  foil.  The  cone 
F  is  usually  applied  to  the 
mouthpiece  to  concentrate 
the  sound-waves  upon  the 
disk  D. 

Now,  when  a  person 
directs  his  voice  toward 
the  mouthpiece,  the  aerial 
waves  cause  the  disk  D  to  participate  in  every  motion  made  by  the 
particles  of  air  as  they  beat  against  it,  and  the  motion  of  the  disk  is  com- 
municated by  the  style  to  the  tin  foil,  pro- 
ducing thereon  impressions  or  indenta- 
tions as  it  passes  on  the  rotating  cylinder. 
The  result  is  that  there  is  left  upon  the 
foil  an  exact  representation  of  every  move- 
ment made  by  the  style.  Some  of  the 
indentations  are  quite  perceptible  to  the 
naked  eye,  while  others  are  visible  only 


FIG.  154. 


FIG.  155. 


with  the  aid  of  a  microscope  of  high  power.  Fig.  156  represents  a  piece 
of  the  foil  as  it  would  appear  inverted  after  the  indentations  (here  greatly 
exaggerated)  have  been  imprinted  upon  it. 

The  words  addressed  to  the  phonograph  having  been  thus  impressed 
upon  the  foil,  the  mouthpiece  and  style  are  temporarily  removed,  while 
the  cylinder  is  brought  back  to  the  position  it  had 
when  the  talking  began,  and  then  the  mouthpiece 
is  replaced.  Now,  evidently,  if  the  crank  be  turned 
in  the  same  direction  as  before,  the  style,  resting 
upon  the  foil  beneath,  will  be  made  to  play  up  and  down  as  it  passes  over 
ridges  and  sinks  into  depressions  ;  this  will  cause  the  disk  D  to  reproduce 
the  same  vibratory  movements  that  caused  the  ridges  and  depressions  in 
the  foil.  The  vibrations  of  the  disk  are  communicated  to  the  air,  and 
through  the  air  to  the  ear  ;  thus  the  words  spoken  to  the  apparatus  may 
be,  as  it  were,  shaken  out  into  the  air  again  at  any  subsequent  time, 
even  centuries  after,  accompanied  by  the  exact  accents,  intonations,  and 
quality  of  sound  of  the  original. 


FIG. 156. 


MUSICAL   INSTRUMENTS.  199 

Subsequently  Edison  improved  this  instrument  by  replacing  the  metal- 
lic foil  by  a  cylinder  of  hard  wax  composition,  rotating  it  by  an  electric 
motor,  and  providing  an  improved  form  of  style,  which  engraves  upon 
the  wax  the  most  delicate  variations  of  vibratory  motions,  arid  thus,  as  it 
were,  reproduces  speech  and  musical  notes  with  all  their  delicate  shades 
of  expression  and  modulation. 


SECTION  XII. 

MUSICAL  INSTRUMENTS. 

205.  Classification  of  Musical  Instruments.     Musical   in- 
struments may  be  grouped  into  three  classes :  (1) 
stringed  instruments ;    (2)   wind   instruments,  in 

which  the  sound  is  due  to  the  vibration  of  columns 
of  air  confined  in  tubes ;  (3)  instruments  in  which 
the  vibrator  is  a  membrane  or  plate.  The  first 
class  has  received  its  share  of  attention  ;  the  other 
two  merit  a  little  further  consideration. 

206,  Wind  Instruments. 

The  pitch  of  vibrating  air-columns,  as  well  as  of 
strings,  varies  with  the  length,  and  (1)  in  both 
stopped1  and  open1  pipes  the  number  of  vibrations 
is  inversely  proportional  to  the  length  of  the  pipe. 
(2)  An  open  pipe  gives  a  note  an  octave  higher  than 
a  closed  pipe  of  the  same  length. 

Fig.  157  represents  an  open  organ-pipe  provided  with  a 
glass  window,  A,  in  one  of  its  sides.     A  wire  hoop,  B,  has 
stretched  over  it  a  membrane,  and  the  whole  is  suspended 
by  a  thread  within  the  pipe.     If  the  membrane  be  placed 
near  the  upper  end,  a  buzzing  sound  proceeds  from  the       FlG>  157> 
membrane  when  the  fundamental  tone  of  the  pipe  is  sounded  ;  and  sand 
placed  on  the  membrane  dances  up  and  down  in  a  lively  manner.     If  the 
membrane  be  lowered,  the  buzzing  sound  becomes  fainter,  till,  at  the 

1  The  terms  "  stopped  "  and  "  open  "  apply  to  only  one  end  of  the  pipe ;  the  other, 
in  both  kinds,  is  always  open. 


200 


MOLAR    DYNAMICS. 


middle  of  the  tube,  it  ceases  entirely,  and  the  sand  becomes  quiet.  If 
the  membrane  be  lowered  still  further,  the  sound  and  dancing  recom- 
mence, and  increase  as  the  lower  end  is  approached. 

(3)  When  the  fundamental  tone  of  an  open  pipe  is  produced, 
its  air-column  divides  into  two  equal  vibrating  sections,  with  the 
anti-nodes  at  the  extremities  of  the  tube,  and  a  node  in  the 
middle. 

If  the  pipe  be  stopped,  there  is  a  node  at  the  stopped  end ;  if  it  be 
open,  there  is  an  anti-node  at  the  open  end  ;  and  in  both  cases  there  is 
ari  anti-node  at  the  end  where  the  wind  enters,  which  is  always,  to  a 
certain  extent,  open. 

A,  B,  and  C  of  Fig.  158  show,  respectively,  the  positions  of  the  nodes 
and  anti-nodes  for  the  fundamental  tone  and  the  first  and  second  over- 
tones of  a  closed  pipe  ;  and  A',  B',  and  C'  show  the  positions  of  the  same 


c' 


FIG.  158. 


in  an  open  pipe  of  the  same  length.  The  distance  between  the  dotted 
lines  shows  the  relative  amplitudes  of  the  vibrations  of  the  air  particles  at 
various  points  along  the  tube.  Now,  the  distance  between  a  node  and 
the  nearest  anti-node  is  a  quarter  of  a  wave-length.  Comparing,  then, 
A  and  A',  it  will  be  seen  that  the  wave-length  of  the  fundamental  of 


SOUNDING   PLATES. 


201 


the  closed  pipe  must  be  twice  the  wave-length  of  the  fundamental 
of  the  open  pipe  ;  hence,  the  vibration-period  of  the  latter  is  half  that  of 
the  former  ;  consequently,  the  fundamental  of  the  open  pipe  must  be  an 
octave  higher  than  that  of  the  closed  pipe. 

207.  Sounding  Plates,  etc. 

Experiment.  Fasten  with  a  screw  the  elastic  brass  plate  A  (Fig.  159) 
on  the  upright  support.  Strew  fine  sand  over  the  plate,  draw  a  rosined 
bass  bow  steadily  and  firmly  over  one  of  its  edges  near  a  corner,  and 


FIG.  159. 

at  the  same  time  touch  the  middle  of  one  of  its  edges  with  the  tip  of 
the  finger ;  a  musical  sound  will  be  produced,  and  the  sand  will  dance 
up  and  down,  and  quickly  collect  in  two  rows,  extending  across  the 
plate  at  right  angles  to  each  other.  Draw  the  bow  across  the  middle  of 
an  edge,  and  touch  with  a  finger  one  of  its  corners  ;  the  sand  will  ar- 
range itself  (2)  in  two  diagonal  rows  across  the  plate.  Touch,  with  the 
nails  of  the  thumb  and  a  finger,  two  points  on  one  edge  of  the  plate 
as  shown  in  the  figure,  and  draw  the  bow  across  the  middle  of  one 
of  the  other  edges,  and  you  will  obtain  additional  rows  and  a  shriller 
note. 

By  varying  the  position  of  the  points  touched  and  bowed,  a 
great  variety  of  patterns  can  be  obtained.  It  will  be  seen  that 
the  effect  of  touching  any  point  with  a  finger  is  to  prevent  vibra- 
tion at  that  point,  and  "consequently  a  node  is  there  produced. 


202 


MOLAR    DYNAMICS. 


FIG.  60. 


The  whole  plate  then  divides  itself  up  into  segments  with 
nodal  division  lines  in  conformity  with  the  node  thus  formed. 
The  sand  rolls  away  from  those  parts  which  are  alternately 

thrown  into  crests  and  troughs,  to  the  parts 

that  are  at  rest. 

208.  Bells.  A  bell  or  goblet  is  subject  to 
the  same  laws  of  vibration  as  a  plate.  If  a 
goblet  partly  filled  with  water  be  bowed  at 
some  point,  the  surface  of  the  water  will 
become  rippled  with  wavelets  (Fig.  160) 
radiating  from  four  points  90°  apart,  corre- 
sponding to  the  centers  of  four  venters  into 
which  the  goblet  becomes  divided,  and  sprays 
of  water  will  be  thrown  from  the  four  quadrants. 

SECTION  XIII. 
VOCAL   ORGANS.      THE   EAR. 

209.  Vocal  Organs.  The  organ  of  the  voice  is  a  reed  in- 
strument situated  at  the  top  of  the  windpipe  or  trachea.  A 
pair  of  elastic  bands,  a  a  (Fig.  161), 
called  the  vocal  chords,  is  stretched 
across  the  top  of  the  windpipe.  The 
air-passage  b  between  these  chords  is 
freely  open  while  a  person  is  breath- 
ing ;  but  when  he  speaks  or  sings,  they 
are  brought  nearly  together  so  as  to 
leave  only  a  narrow  slit-like  opening, 
thus  making  a  sort  of  double  reed, 
which  vibrates  when  air  is  forced  from 
the  lungs  through  the  narrow  passage, 
somewhat  like  the  little  tongue  of  a 
toy  trumpet.  The  sounds  are  grave  or  high  according  to  the 
tension  of  the  chords,  which  is  regulated  by  muscular  action. 


FIG.  161. 


THE   EAR.  203 

The  cavities  of  the  mouth  and  the  nasal  passages  form  a 
compound  resonance  tube.  This  tube  adapts  itself,  by  its 
varying  width  and  length,  to  the  pitch  of  the  notes  produced 
by  the  vocal  chords.  The  different  qualities  of  the  different 
vowel  sounds  are  produced  by  the  varying  forms  of  the  reso- 
nating mouth-cavity,  the  pitch  of  the  fundamental  tones  given 
by  the  vocal  chords  remaining  the  same.  This  constitutes 
articulation. 

210.  The  Ear.  At  the  inner  end  of  the  outer  ear-passage  C 
is  the  thin  membrane  D,  known  as  the  "  drum  of  the  ear," 
which  serves  as  a  partition  between  the  outer  ear-passage  and 


FIG. 162. 


the  cavity  K  of  the  middle  ear.  A  chain  of  tiny  bones  stretches 
across  this  cavity  from  the  drum  to  another  membranous 
partition  which  closes  the  orifice  of  the  inner  ear.  N  is  the 
Eustachian  tube  connecting  the  middle  ear-cavity  with  the 
back  part  of  the  throat  ;  T  T  are  auditory  nerves.  The  middle 
ear  contains  air,  and  the  Eustachian  tube  forms  a  means  of 
ingress  and  egress  far  air  through  the  throat.  The  inner 
ear  is  filled  with  a  transparent  liquid. 


204  MOLAR   DYNAMICS. 

Now,  how  does  the  ear  hear  ?  and  how  is  it  able  to  dis- 
tinguish between  the  infinite  variety  of  aerial  sound-waves  so 
as  to  interpret  correctly  the  corresponding  quality,  pitch,  and 
loudness  of  sound  ?  Sound-waves  enter  the  external  ear- 
passage  C  as  ocean  waves  enter  the  bays  of  the  seacoast,  are 
reflected  inward,  and  strike  the  drum.  The.  air  particles, 
beating  against  this  drum,  impress  upon  it  the  precise  wave- 
form that  is  transmitted  to  it  through  the  air  from  the  sound- 
ing body.  The  motion  received  by  the  drum  is  transmitted  by 
the  air  in  the  middle  ear-cavity  and  by  the  chain  of  bones  to  the 
membranous  wall  of  the  inner  ear.  From  the  walls  of  the 
inner  ear  project  into  its  liquid  contents  thousands  of  fine 
elastic  threads  or  fibers,  called  "rods  of  Corti."  These  vibratile 
fibers  vary  in  length  and  size,  and  are  therefore  suited  to  re- 
spond sympathetically  to  a  great  variety  of  vibration-periods. 
The  auditory  nerve  at  this  extremity  is  divided  into  a  large 
number  of  filaments,  like  a  cord  unraveled  at  its  end,  and  one 
of  these  filaments  is  attached  to  each  fiber.  Now,  as  the 
sound-waves  reach  the  membranous  wall  of  the  inner  ear  they 
set  it,  and  by  means  of  it  the  liquid  contents  of  the  inner  ear, 
into  forced  vibration,  and  so  through  the  liquid  the  immersed 
fibers  receive  impulses.  Those  fibers  whose  vibration-periods 
correspond  to  the  constituents  of  the  compound  wave  are 
thrown  into  sympathetic  vibration.  The  fibers  stir  the  nerve- 
filaments,  and  these  transmit  the  impression  to  the  brain, 
where  in  some  mysterious  manner  these  disturbances  are 
interpreted  as  sound  of  definite  pitch,  quality,  and  intensity. 

EXERCISES. 

1.  Your  ear  can  easily  distinguish  a  note  sounded  by  a  violin  from 
the  same  note  produced  by  a  flute.     Explain  the  cause  of  this  difference. 

2.  What  conditions  must  be  fulfilled  that  a  vibrating  body  may  pro- 
duce (a)  sound,  (&)  a  musical  note  ? 

3.  Explain  (a)  why,  when  a  tuning  fork  is  struck  and  the  stem  is 
pressed  against  a  table,  it  sounds  much  louder  than  when  held  in  the 


EXERCISES.  205 

hand  ;  (6)  why  the  sound  in  the  former  case  does  not  continue  so  long  as 
in  the  latter. 

4.  State  whether  or  not  the  velocity  of  sound  in  air  is  affected  (a)  by 
the  hight  of  the  barometric  column,  (6)  by  the  temperature  of  the  air; 
give  reasons  for  your  answer  in  each  case. 

5.  The  disturbance  produced  in  the  surrounding  air  by  a  sounding 
body  has  been  likened  to  that  caused  in  a  pool  by  a  stone  thrown  into 
the  water.     Point  out  in  what  particulars  the  motions  of  the  air  and  of 
the  water  in  the  two  cases  are  really  similar,  and  in  what  dissimilar. 

6.  The  tone  given  out  by  an  open  pipe  3  inches  long  is  found  to  be 
caused  by  2220  vibrations  per  second.     Calculate  from  these  data  the 
velocity  of  sound  in  air. 

7.  When  a  sounding  body  and  the  ear  approach  each  other,  or  recede 
from  each  other,  the  pitch  of  the  sound  appears  to  change.     Explain. 

8.  How  is  an  ear  trumpet  related  to  a  speaking  trumpet  ? 

9.  Represent  by  diagrams  (a)  two  waves  which  have  the  same  wave- 
length, but  of  which  one  has  twice  the  amplitude  of  the  other ;  also  (6) 
two  waves  which  have  the  same  amplitude,  but  of  which  one  has  double 
the  wave-length  of  the  other. 

10.  Which  is  the  better  conductor  of  sound,  sawdust  or  solid  wood  ? 
Why? 

11.  (a)  When  a  bottle  of  soda-water  is  opened  a  loud  sound  is  heard. 
Explain.     (6)  Is  it  a  musical  sound  ?    Explain. 

12.  At  one  end  of  a  very  long  tube  a  pistol  is  fired.     Explain  how  it  is 
that  an  observer  at  the  other  end  of  the  tube  hears  the  report  twice. 

13.  If  a  person  set  his  watch  by  the  striking  of  a  clock  half  a  mile 
distant,  when  the  temperature  of  the  air  is  20°  C. ,  what  will  be  the  mag- 
nitude of  the  error  ? 

14.  A  rifle  is  discharged  and  the  echo  produced  by  a  cliff  is  heard  in 
8  seconds.     The  temperature  of  the  air  is  16°  C.     What  is  the  distance 
of  the  cliff  ? 

15.  The  waves  produced  by  a  man's  voice  in  common  conversation 
are  from  8  to  12  feet  long.     Find  the  corresponding  numbers  of  vibrations, 
assuming  the  velocity  of  sound  to  be  1128  feet  per  second. 

16.  The  maximum  resonance  of  a  certain  tuning  fork  is  produced 
when  it  is  placed  over  a  jar  15  inches  high.     How  many  vibrations  does 
this  fork  make  in  a  second  ? 

17.  The  length  of  the  fundamental  wave  of  a  closed  pipe  is  how  many 
times  the  length  of  the  pipe  ? 

18.  Upon  what  does  the  pitch  of  an  organ  pipe  depend  ? 

19.  What  change  occurs  in  the  pitch  of  the  sound  made  by  a  circular 
saw  on  entering  a  plank  ?     Explain. 


CHAPTER   VI. 

ENERGY  OF  ETHER-STRAIN.    RADIANT  ENERGY. 

LIGHT. 

SECTION   I. 
RADIANT   ENERGY. 

211.  The  Ether.     We  know  matter  by  its   properties  ;   in 
other  words,  the  existence  of  any  form  of  matter  is  to  us  only 
an  inference  from  the  phenomena  to  which  it  gives  rise.     By 
evidence  of  a  similar  nature  we  are  led  to  believe  in  the 
existence  of  a  medium  called  the  ether,  pervading  all  space 
and  penetrating  between  the  molecules  of  matter,  which  are 
imbedded  in  it  and  surrounded  by  it  as  the  earth  is  surrounded 
by  its  atmosphere.     We  cannot  see,  hear,  feel,  taste,  smell, 
exhaust,  weigh,  or  measure  it ;  yet   all  this,  paradoxical  as  it 
may  seeni,  furnishes  absolutely  no  evidence  that  it  does  not 
exist. 

Phenomena  occur  just  as  they  would  occur  if  all  space  were 
filled  with  a  medium  capable  of  transmitting  motion  and 
energy,  and  we  can  account  for  all  these  phenomena  on  no 
other  hypothesis;  hence  our  belief  in  the  existence  of  the 
medium.  The  ether  is  a  medium  for  the  transmission  of 
energy  in  the  form  of  vibrations.1 

212.  Radiation.    Radiant  Energy.     The    ether   is    set    in 
vibration  by  the  motion  of  the  molecules  of  matter.     This 
local   disturbance    creates   ether-waves,  and  by  these  waves 
energy  is    transferred   from   body  to  body   by   the   process 

1  The  following  is  Lord  Salisbury's  witty  definition  :  "  Ether  is  the  nominative  case 
of  the  verb  '  to  vibrate.'  " 


EFFECTS    OF   RADIANT   ENERGY.  207 

called  radiation.  Energy  so  transmitted  is  called  radiant 
energy,  and  the  body  thus  emitting  energy  is  called  a  radia- 
tor. Radiant  energy  can  be  transformed  into  any  other  form 
of  energy,  and  therefore  offers  no  exception  to  the  doctrine 
of  correlation  of  energy. 

213.  Effects  of  Radiant  Energy.  When  radiant  energy  is 
received  upon  the  surfaces  of  our  bodies,  warmth  is  felt ; 
when  received  upon  the  bulb  of  a  thermometer,  rise  of  tem- 
perature is  indicated  ;  when  received  by  the  eye,  the  sense  of 
sight  may  be  affected  ;  if  it  is  received  upon  sensitive  photo- 
graphic plates,  upon  the  leaves  of  plants,  or  upon  various 
chemical  mixtures,  chemical  changes  may  be  promoted.  Thus 
it  seems  that  when  ether-waves  impinge  upon  objects  their 
energy  is  transformed,  producing  effects  of  different  kinds, 
which  are  determined  by  the  nature  of  the  body  upon  which 
they  fall.  The  effect  which  most  concerns  us  is  that  pro- 
duced when  the  radiations  strike  the  eye  and  become  the 
means,  through  this  organ,  of  creating  the  sensation  of  sight. 
The  eye  is  an  ether  sense-organ,  much  as  the  ear  may  be 
regarded  as  an  air  sense-organ. 


SECTION   II. 

LIGHT. 

214.  Light  Defined.  Hypotheses.  Two  widely  different 
hypotheses  regarding  the  nature  of  light  have  been  pro- 
pounded. One,  the  so-called  emission  or  corpuscular  hypothesis, 
was  supported  by  Newton  (1672),  and  by  most  physicists  up 
to  the  early  part  of  the  present  century.  It  assumes  that  a 
luminous  body  (e.g.  the  sun)  emits  minute  material  particles 
(corpuscles)  which  travel  through  space  in  all  directions  with 
immense  velocity,  and  that  these  particles  by  their  impact 
upon  the  eye  produce  the  sensation  of  sight.  As  a  rose  emits 


208 


ETHEK  DYNAMICS. 


minute  particles  which,  reaching  the  nostrils,  enable  us  to 
smell  the  rose,  so  a  star  is  supposed  to  emit  corpuscular 
matter  which,  on  reaching  the  eye,  enables  us  to  see  the  star. 
This  hypothesis  is  now  discarded  by  scientists.  The  theory 
which  obtains  at  the  present  time,  called  the  undulatory  or 
wave-theory,  is  based  upon  the  hypothesis  that  energy  is  trans- 
mitted from  body  to  body,  e.g.  from 
the  sun  to  the  earth,  in  the  form  of 
vibrations  or  wave-action  in  the  all- 
pervading  ether.  According  to  the 
latter  theory,  light  is  that  vibration  of 
the  ether  which  may  be  appreciated  by 
the  organ  of  sight.1 

215.  Luminous  and  Illuminated 
Objects.  Some  bodies  are  seen  by 
means  of  light-waves  which  they  gen- 
erate, e.g.  the  sun,  a  candle  flame,  and 
a  "live  coal "  ;  they  are  called  lumi- 
nous bodies.  Others  are  seen  only 
by  means  of  light-waves  which  they 
receive  from  luminous  bodies  and 
reflect  to  the  eye,  and,  when  thus 

rendered  visible,  are  said  to  be  illuminated ;  e.g.  the  moon,  a 

man,  a  cloud,  and  a  "  dead  "  coal. 

216,  Light-waves  Travel  in  Straight  Lines.  The  paths  of 
light-waves  admitted  into  a  darkened  room  through  a  small 
aperture,  as  indicated  by  the  illuminated  dust,  are  perfectly 
straight.  An  object  is  seen  by  means  of  light-waves  which  it 

1  It  will  be  shown  further  on  (§  252)  that  not  all  ether-waves  are  capable  of  affecting 
the  sight;  hence,  for  the  purpose  of  distinction  we  apply  the  term  light-waves  to  those 
ether-waves  only  which  are  capable  of  producing  vision.  It  is  strongly  recommended 
that  the  student  in  beginning  this  branch  of  science  make  use  of  the  term  light-waves 
instead  of  light,  except  when  such  usage  would  lead  to  an  inconvenient  circumlocu- 
tion, in  order  that  he  may  have  strongly  impressed  upon  his  mind  the  fact  that  when 
he  is  dealing  with  light  he  is  dealing  with  waves. 


HAY,    BEAM,    PENCIL.  209 

sends  to  the  eye.  A  small  object  placed  in  a  straight  line 
between  the  eye  and  a  luminous  point  may  intercept  the  light- 
waves in  that  path,  so  that  the  point  becomes  invisible. 
Hence  we  cannot  see  around  a  corner  or  through  a  bent  tube. 

217.  Ray,  Beam,  Pencil.     Any  line,  R  R  (Fig.  163),  which 
pierces  the  surface  of  an  ether-wave  front,  a  b,  perpendicularly, 
is  called  a  ray.      The  term  "  ray  "  is  but  an  expression  for  the 
direction  in  which  motion  is  propagated,  and  along  which  the 
successive  effects  of  ether-waves  occur.1      If  the  wave-surface 
a'  b'  be  a  plane,  the  rays  R'  R'  are  parallel,  and  a  collection 
of  such  rays  is  called  a  beam.     If  the  wave-surface  a"  b"  be 
spherical,  the  rays  R"  R"  have  a  common  point  at  the  center 
of  curvature  ;  and  a  collection  of  such  rays  is  called  a  pencil. 

218.  Transparent,    Translucent,   and   Opaque   Substances. 

Substances  are  transparent,  translucent,  or  opaque  according 
to  the  manner  in  which  they  act  upon  the  light-waves  which 
are  incident  upon  them.  .  Generally  speaking,  those  sub- 
stances are  transparent  that  allow  objects  to  be  seen  through 
them  distinctly,  e.g.  air,  glass,  and  water.  Those  substances 
are  translucent  that  allow  light-waves  to  pass,  but  in  such  a 
scattered  condition  that  objects  are  not  seen  distinctly  through 
them,  e.g.  fog,  ground  glass,  and  oiled  paper.  Those  sub- 
stances are  opaque  that  apparently  cut  off  all  the  light-waves 
and  prevent  objects  from  being  seen  through  them.  When 
bodies  intercept  light,  they  are  said  to  cast  shadows. 

219.  Every   Point   of  a  Luminous  Body  an  Independent 
Source  of  Light- waves.     Place  a  candle  flame  in  the  center 
of  a  darkened  room  ;  each  wall  and  every  point  of  each  wall 
becomes  illuminated.     Place  yourself  in  any  part  of  the  room, 

1  In  dealing  with  certain  phenomena  (e.g.  reflection  of  light)  we  may,  to  facilitate 
our  study,  consider  the  light  as  propagated  in  straight  lines  or  rays  ;  but  we  must 
bear  in  mind  that  a  ray  has  no  material  or  physical  existence,  for  it  is  a  wave  that 
is  propagated,  not  a  ray. 


210 


ETHER   DYNAMICS. 


i.e.  in  any  direction  from  the  flame  ;  you  are  able  to  see  not 

only  the  flame,  but  every  point 
of  the  flame  ;  hence  every  point 
of  the  flame  must  emit  light- 
waves in  every  direction.  Every 
point  of  a  luminous  body  is  an 
independent  source  of  light-waves, 
and  emits  them  in  every  direc- 
tion. Such  a  point  is  called  a 
luminous  point.  In  Fig.  164 
there  are  represented  a  few  of 
the  infinite  number  of  pencils 
of  light  emitted  by  three  lumi- 
nous points. 


FIG.  164. 


220.  Images  Formed  through  Small  Apertures. 

Experiment  1.  Cut  a  hole  about  8  cm.  square  in  one  side  of  a  box  ; 
cover  the  hole  with  tin  foil,  and  prick  a  hole  in  the  foil  with  a  pin. 
Place  the  box  in  a  darkened  room,  and  a  candle  flame  in  the  box  near 
the  pin  hole.  Hold  an  oiled-paper  screen  before  the  hole  in  the  foil ;  an 
inverted  image  of  the  candle  flame  will  appear  upon  the  translucent 
paper.  An  image  is  a  kind  of  picture  of  an  object. 

If  light-waves  from  objects  illuminated  by  the  sun — e.g. 
trees,  houses,  clouds,  or  even  from  an  entire  landscape  —  be  al- 
lowed to  pass  through  a  small 
aperture  in  a  window  shutter 
and  strike  a  white  screen  (or 
a  white  wall)  in  a  dark  room, 
inverted  images  of  the  objects 
in  their  true  colors  will  appear 
upon  the  screen.  The  cause 
of  these  phenomena  is  easily 
understood.  When  no  screen 
intervenes  between  the  candle  and  the  screen  A  (Fig.  165), 
every  point  of  the  screen  receives  light  from  every  point 


FIG. 165. 


SHADOWS. 


211 


of  the  candle  ;  consequently,  at  every  point  on  A,  images 
of  all  the  points  of  the  candle  are  formed.  The  result  of 
the  confusion  of  images  is  that  no  image  is  distinguish- 
able. But  let  the  screen  B,  containing  a  small  hole,  be 
interposed;  then,  since  light  travels  only  in  straight  lines, 
the  point  Y'  can  receive  an  image  only  of  the  point  Y,  the 
point  Z'  only  of  the  point  Z,  and  so  for  intermediate  points  ; 
hence  a  distinct  image  of  the  object  must  be  formed  on  the 
screen  A.  That  an  image  may  be  distinct,  the  images  of  differ- 
ent points  of  the  object  must  not  mix,  and  therefore  all  rays 
from  each  point  on  the  object  must  be  carried  to  the  correspond- 
ing point  on  the  image. 

221.  Shadows. 

Experiment  2.  Procure  a  piece  of  tin  or  cardboard  18  cm.  square  ; 
place  it  between  a  white  wall  and  a  candle  flame  in  a  darkened  room. 
The  opaque  tin  intercepts  the  light  that  strikes  it,  and  thereby  excludes 
light  from  a  space  behind  it. 


FIG.  166. 


This  space  is  called  a  shadow.  That  portion  of  the  surface 
of  the  wall  that  is  darkened  is  a  section  of  the  shadow,  and 
represents  in  form  a  cross  section  of  the  body  that  intercepts 
the  light.  A  section  of  a  shadow  is  frequently  for  conven- 


212  ETHER 'DYNAMICS. 

ience  called  a  shadow.  Notice  that  the  shadow  is  made  up 
of  two  distinct  parts  —  a  dark  center,  bordered  on  all  sides 
by  a  much  lighter  fringe.  The  dark  center  is  called  the 
umbra,  and  the  lighter  envelope  is  called  the  penumbra. 

The  umbra  is  the  part  of  a  shadow  that  gets  no  light  from 
the  luminous  body,  while  the  penumbra  is  the  part  that  gets 
light  from  some  portion  of  the  body,  but  not  from  the  whole. 

Let  A  B  (Fig.  166)  represent  a  luminous  body,  and  C  D  an  opaque 
body.  The  pencil  from  the  luminous  point  A  will  be  intercepted  between 
the  lines  C  F  and  D  G,  and  the  pencil  from  B  will  be  intercepted  between 
the  lines  C  E  and  D  F.  Hence  the  light  will  be  wholly  excluded  only 
from  the  space  between  the  lines  C  F  arid  D  F,  which  enclose  the  umbra. 
The  enveloping  penumbra,  a  section  of  which  is  included  between  the 
lines  C  E  and  C  F,  and  between  D  F  and  D  G,  receives  light  from  certain 
points  of  the  luminous  body,  but  not  from  all. 

222.  Speed  of  Light.  That  light  travels  with  finite  speed 
was  first  established  in  1676  by  the  Danish  astronomer 
Koemer,  then  engaged  in  Paris  in  observing  the  eclipses  of 
Jupiter's  moons.  He  made  observations  on  that  one  of  the 
five  of  Jupiter's  satellites  which  is  nearest  to  the  planet,  and 
which  revolves  round  this  planet  as  the  moon  does  round  the 
earth.  At  regular  intervals  the  satellite  passes  behind  the 
planet  and  is  eclipsed  within  its  shadow.  The  observed 
intervals,  however,  were  found  to  be  shorter  than  the  mean 
value  when  the  earth  and  Jupiter  were  approaching  each 
other,  and  longer  when  they  were  receding  from  each  other. 
It  was  evident  that  this  difference  was  due  to  the  time  con- 
sumed by  the  light  in  crossing  the  intervening  spaces.  From 
the  results  of  these  observations  it  was  calculated  that  light 
required  16  minutes  and  36  seconds  to  traverse  the  diameter 
of  the  earth's  orbit,  approximately  185,000,000  miles.  The 
speed  of  light  thus  determined  is  192,500  miles  per  second. 
It  has  been,  determined  by  later  experiments  and  more 
reliable  methods  that  this  value  is  too  great.  The  result 


EXERCISES.  213 

obtained  by  Michelson  by  experimental  methods  is  about 
186,380  miles  per  second.  This  may  be  accepted  as  probably 
the  nearest  approximation  yet  made  to  the  true  speed  of  light 
in  a  vacuum.  At  this  rate,  light  would  encircle  our  earth 
between  seven  and  eight  times  in  a  second. 

EXERCISES. 

1.  Why  are  images  formed  through  apertures  inverted  ? 

2.  Why  is  the  size  of  the  image  dependent  on  the  distance  of  the 
screen  from  the  aperture  ? 

3.  Why  does  an  image  become  dimmer  as  it  becomes  larger  ? 

4.  Why  do  we  not  imprint  an  image  of  our  person  on  every  object  in 
front  of  which  we  stand  ? 

5.  Upon  what  fact  does  a  gunner  rely  in  taking  sight  ? 

6.  Explain  the  umbra  and  penumbra  cast  by  the  opaque  body  H  I, 
Fig.  166. 

7.  When  will  a  transverse  section  of  the  umbra  of  an  opaque  body  be 
larger  than  the  object  itself  ? 

8.  When  has  an  umbra  a  limited  length  ? 

9.  What  is  the  shape  of  the  umbra  cast  by  the  sphere  C  D,  Fig.  166  ? 

10.  If  C  D  should  become  the  luminous  body,  and  A  B  a  non-luminous 
opaque  body,  what  changes  would  occur  in  the  umbra  and  the  shadow 
cast? 

11.  Why  is  it  difficult  to  determine  the  exact  point  on  the  ground 
where  the  umbra  of  a  church  steeple  terminates  ? 

12.  What  is  the  shape  of  a  section  of  the  shadow  cast  by  a  circular 
disk  placed  obliquely  between  a  luminous  body  and  a  screen  ?     What  is 
its  shape  when  the  disk  is  placed  edgewise  ? 

13.  The  section  of  the  earth's  umbra  on  the  moon  in  an  eclipse  always 
has  a  circular  outline.     What  does  this  show  respecting  the  shape  of  the 
earth? 

14.  (a)  The  sensation  of  sound  is  how  produced  ?     (6)  How  is  the 
sensation  of  sight  produced  ?     (c)    How  are  sound-waves  produced  ? 
(d)  How  are  light-waves  produced  ?     (e)  Which,  sound-waves  or  ether- 
waves,  originate  in.  molecular  vibrations?     (/)  Sound-waves  travel  in 
what  mediums  ?     (g)  Light-waves  travel  only  in  what  medium  ? 

15.  (a)  What  is  radiant  energy?     (6)    Do  all  bodies   emit  radiant 
energy  ?     (c)  Do  all  ether-waves  affect  the  sight  ?     (d)  Do  all  bodies 
generate  light-waves  ?     (e)  Is  a  "dead  coal"  seen  by  ether-waves  which 
it  generates  ? 


214  ETHER    DYNAMICS. 

SECTION    III. 
INTENSITY   OF   ILLUMINATION. 

223.  Application  of  the  Law  of  Inverse  Squares  to  Light. 

Light  diminishes  in  intensity,  and  hence  in  its  power  to 
illuminate  objects  which  it  strikes,  as  it  recedes  from  its 
source.  The  intensity  of  light  diminishes  as  the  square  of  the 
distance  from  its  source  increases.  Calling  the  quantity  of 
light  falling  upon  a  visiting  card  at  a  distance  of  2  feet  from 
a  lamp  flame  1,  the  quantity  falling  upon  the  same  card  at  a 
distance  of  4  feet  is  £,  at  a  distance  of  6  feet  it  is  £,  and  so 
on.  This  is  the  meaning  of  the  law  of  inverse  squares,  as 
applied  to  light. 

This  law  may  be  illustrated  thus :  A  square  card  placed  (say)  1  foot 
from  a  certain  point  in  a  candle  flame,  as  at  A  (Fig.  167),  receives  from 
this  point  a  certain  quantity  of  light.     The 
same  light  if  not  intercepted  would  go  on  to 
B,  at  a  distance  of  2  feet,  and  would  there 
illuminate  four  squares,  each  of  the  size  of  the 
card,  and  being  spread  over  four  times  the 
area  can  illuminate  each  square  with  only  one 
Fio.  167.  fourth  the  intensity.      If  allowed  to  proceed 

to  C,  3  feet  distant,  it  illuminates  nine  such  squares,  and  has  but  one 
ninth  its  intensity  at  A.  The  law  is  strictly  true  only  when  distance 
from  individual  points  is  considered. 

224.  Unit  of  Measurement.     The  unit  generally  employed 
in  the  measurement  of  the  illuminating  power  of  the  light 
emitted  by  a  luminous  body  is  the  British  candle-power.     It 
is  the  illuminating  power  of  a  sperm  candle  }  in.  in  diameter, 
burning  120  grains  to  the  hour. 

225.  Photometry.     The  law  just  established  enables  us  to 
compare  the  illuminating   power  of  one  light  with  that  of 
another,   and   to  express  by  numbers  their  relative  illumi- 
nating   powers.     The    process    is    called   photometry    (light- 
measuring),  and  the  instrument  employed,  a  photometer. 


QUESTIONS. 


215 


The  Bunsen  photometer  (Fig.  168)  has  a  screen  of  paper,  S, 
mounted  in  a  box,  B,  open  in  front  and  at  the  two  ends.  The 
box  slides  on  a  graduated  bar.  The  screen  has  a  circular 
central  spot  saturated  with  paraffine,  which  renders  the  spot 
more  translucent  than  other  portions  of  the  screen.  One  side 
of  the  screen  is  illuminated  by  the  light  L,  whose  intensity  is 


FIG.  168. 

to  be  measured,  and  the  other  side  by  a  standard  candle,  L'. 
When  the  screen  is  so  placed  that  the  two  sides  are  equally 
illuminated  by  the  two  lights,  the  paraffined  spot  becomes 
nearly  invisible.  When  one  side  is  more  strongly  illuminated 
than  the  other,  the  spot  appears  dark  on  that  side  and  light 
on  the  other.  The  candle-power  of  the  two  lights  is  directly 
proportional  to  the  square 
of  their  respective  distances  — — — 
from  the  screen  when  it  is 
equally  illuminated  on  both 


In  order  to  render  both 
sides  of  the  disk  simulta- 
neously visible,  two  mir- 
rors, m  and  m'  (Fig.  169),  are  placed  in  the  box  in  a  vertical 
position  so  as  to  reflect  images  of  the  circular  spot  in  the 
screen  S  to  the  eyes  at  E  EI. 

QUESTIONS. 

1.  Suppose  that  a  lighted  candle  is  placed  in  the  center  of  each  of 
three  cubical  rooms,  respectively  10,  20,  and  30  feet  on  a  side,  would  a 
single  wall  of  the  first  room  receive  more  light  than  a  single  wall  of  either 
of  the  other  rooms,  or  less  ? 


216 


ETHER    DYNAMICS. 


2.  Would  one  square  foot  of   a  wall  of   the  third  room  receive  as 
much  light  as  would  be  received  by  one  square  foot  of  a  wall  of  the  first 
room  ?    If  not,  what  difference  would  there  be,  and  why  the  difference  ? 

3.  If  a  board  10  cm.  square  be  placed  25  cm.  from  a  candle  flame,  the 
area  of  the  shadow  of  the  board  cast  on  a  screen  75  cm.  distant  from  the 
candle  will  be  how  many  times  the  area  of  the  board  ?    Then  the  light 
intercepted  by  the  board  will  illuminate  how  much  of  the  surface  of  the 
screen  if  the  board  be  withdrawn  ? 

4.  Give  a  reason  for  the  law  of  inverse  squares. 

5.  To  what  besides  light  has  this  law  been  found  applicable  ? 

6.  The  two  sides  of  a  paper  disk  are  illuminated  equally  by  a  candle 
flame  50  cm.  distant  on  one  side  and  a  gas  flame  200  cm.  distant  on  the 
other  side,    (a)  Compare  the  intensities  of  the  two  lights  at  equal  dis- 
tances from  their  sources,     (b)   If  the  candle  be  a  standard  candle,  what 
is  the  intensity  of  the  gas  flame  ? 


SECTION   IV. 

APPARENT   SIZE   OF   AN   OBJECT. 

226.  Visual  Angle.  We  see  an  object  by  means  of  its 
image  formed  on  the  retina  of  the  eye  ;  and  its  apparent 
magnitude  is  determined  by  the  extent  of  the  retina  covered 


FIG. 170. 

by  its  image.  Kays  proceeding  from  opposite  extremities  of 
an  object,  as  A  B  (Fig.  170),  meet  and  cross  each  other  within 
the  eye.  Now,  as  the  distance  between  the  points  of  the 
blades  of  a  pair  of  scissors  depends  upon  the  angle  that  the 
handles  form  with  each  other,  so  the  size  of  the  image 
formed  on  the  retina  depends  upon  the  size  of  the  angle, 
called  the  visual  angle,  formed  by  these  rays  as  they  enter 


MIRRORS.  217 

the  eye.  But  the  size  of  the  visual  angle  diminishes  approxi- 
mately as  the  distance  of  the  object  from  the  eye  increases, 
as  shown  in  the  diagram  ;  e.g.  at  twice  the  distance  the  angle 
is  about  one  half  as  great  ;  at  three  times  the  distance  the 
angle  is  one  third  as  great ;  and  so  on.  Hence  distance  affects 
the  apparent  size  of  an  object.  Our  judgment  of  the  size  of 
objects  is,  however,  influenced  by  other  things  besides  the 
visual  angle  which  they  subtend. 

SECTION   V. 

REFLECTION    OF    LIGHT. 

227,  Mirrors.  Images.  Objects  having  polished  surfaces 
which  reflect  light  regularly  (i.e.  do  not  scatter  the  light), 
and  show  images  of  objects  presented  to  them,  are  called 
'mirrors.  The  mirror  itself,  if  clean  and  smooth,  is  scarcely 
visible.  According  to  their  shape,  mirrors  are  called  plane, 
concave,  convex,  spherical)  parabolic,  etc. 

Experiment  1.  (a)  Look  at  the  mirror  M  through  the  hole  marked 
O  in  the  metal  band  (Fig.  171).  You  see  in  the  mirror  an  image  of  the 
hole  through  which  you  look, 
but  you  do  not  see  the  image 
of  any  of  the  other  holes. 
Rays  that  pass  through  this 
hole  strike  the  mirror  perpen- 
dicularly and  are  said  to  be 

normal  to  the  mirror.     Rays  FlG  171 

falling   upon    an    object    are 

called  incident  rays.  The  point  where  a  ray  strikes  is  called  the  point 
of  incidence.  The  reflected  rays  in  this  case  are  thrown  back  in  the 
same  lines  and  through  the  same  hole  that  the  incident  rays  travel. 
Bays  normal  to  a  mirror  after  reflection  simply  retrace  their  own  course, 
(b)  Next  hold  a  candle  flame  at  one  of  the  other  holes,  e.g.  at  the  hole 
marked  10.  You  can  see  the  image  of  the  candle  flame  only  through  the 
hole  of  the  same  number  and  at  an  equal  distance  on  the  other  side. 
The  angle  which  an  incident  ray  makes  with  a  line  normal  at  the  point 
of  incidence  is  called  the  angle  of  incidence,  and  the  angle  made  with 
the  normal  by  a  reflected  ray  is  called  the  angle  of  reflection. 


218 


ETHER    DYNAMICS. 


LAW  OF  REFLECTION.  The  angles  of  incidence  and  reflec- 
tion are  in  the  same  plane,  and  are  equal. 

228.  Diffused  Light, 

Experiment  2.  Introduce  a  small  beam  of  light  into  a  darkened 
room,  and  place  in  its  path  a  mirror.  The  light  is  reflected  in  a  definite 
direction.  If  the  eye  be  placed  so  as  to  receive  the  reflected  light,  it  will 
see,  not  the  mirror,  but  the  image  of  the  sun,  and  the  light  will  be  pain- 
fully intense.  Substitute  for  the  mirror  a  piece  of  unglazed  paper.  The 
light  is  not  reflected  by  the  paper  in  any  definite  direction,  but  is  scat- 
tered in  every  direction,  illuminating  objects  in  the  vicinity  and  rendering 
them  visible.  Looking  at  the  paper,  you  see,  not  an  image  of  the  sun, 
but  the  paper  itself,  and  you  may  see  it  equally  well  from  all  directions. 

The  surface  of  the  paper  receives  light  from  a  definite  direc- 
tion, but  reflects  it  in  every  direction;  in  other  words,  it 
scatters,  or  diffuses,  the  light.  The  difference  in  the  phenom- 
ena in  the  two  cases  is  caused  by  the  difference  in  the 
smoothness  of  the  two  reflecting  surfaces.  A  B  (Fig.  172) 


represents  a  smooth  surface,  like  that  of  glass,  which  reflects 
nearly  all  the  rays  of  light  in  the  same  direction,  because 
nearly  all  the  points  of  reflection  are  in  the  same  plane. 
C  D  represents  a  surface  of  paper  having  the  roughness  of  its 
surface  greatly  exaggerated.  The  various  points  of  reflection 
are  turned  in  every  possible  direction  ;  consequently,  light  is 
reflected  in  every  direction.  Thus,  the  dull  surfaces  of 
various  objects  around  us  reflect  light  in  all  directions,  and 
are  consequently  visible  from  every  side.  Objects  rendered 
visible  by  reflected  light  are  said  to  be  illuminated. 


REFLECTION   FROM   MIRRORS. 


219 


FIG.  173. 


229.  Reflection  from  Plane  Mirrors ;  Virtual  Images.    M  M 
(Fig.   173)  represents   a  plane  mirror,    and  A  B  a  pencil  of 
divergent   rays   proceeding    from   the 

point  A  of  an  object,  AH.  By  erecting 
perpendiculars  at  the  points  of  inci- 
dence, or  the  points  where  these  rays 
strike  the  mirror,  and  making  the 
angles  of  reflection  equal  to  the  angles 
of  incidence,  the  paths  B  C  and  E  C  of 
the  reflected  rays  are  found. 

Every  visible  point  of  an  object 
sends  a  cone  of  rays  to  the  eye.  The 
point  always  appears  at  the  place 
whence  these  rays  seem  to  emerge,  i.e.  at  the  apex  of  the  cone. 
If  the  direction  of  these  rays  be  changed  by  reflection,  or  in 
any  other  manner,  the  point  will  appear  to  be  in  the  direction 
of  the  rays  as  they  enter  the  eye  ;  thus,  the  point  A  appears  to 
lie  in  the  direction  C  D,  and  the  point  H  in  the  direction  C  N. 
The  exact  location  of  these  points  may  be  found  by  continu- 
ing each  pencil  of  rays  behind  the  mirror  until  it  comes  to  a 
point,  C  B  at  D,  C  E  at  N.  Thus,  the  pencils  appear  to 
emanate  from  these  points,  and  the  whole  body  of  light- 
waves received  by  the  eye  seems  to  come  from  an  appar- 
ent object,  N  D,  behind  the  mirror.  This  apparent  object  is 
called  an  image.  An  image  is  a  point  or  a  series  of  points 
from  which  diverging  pencils  of  rays  come  or  appear  to  come. 
As  of  course  no  real  image  can  be  formed  back  of  a  mirror, 
such  an  image  is  called  a  virtual  or  an  imaginary  image.  It 
will  be  seen,  by  construction,  that  an  image  in  a  plane  mirror 
appears  as  far  behind  the  mirror  as  the  object  is  in  front  of  it, 
and  is  of  the  same  size  and  shape  as  the  object. 

230.  Reflection  from  Concave  Mirrors.    Let  M  M'  (Fig.  174) 
represent  a  section  of  a  concave  spherical  mirror,  which  may 
be  regarded  as  a  small  part  of  a  hollow  spherical  shell  having 


220  ETHER    DYNAMICS. 

a  polished  interior  surface.  The  distance  in  a  straight  line 
from  M  to  M'  is  called  the  diameter  of  the  mirror.  C  is  the 
center  of  the  sphere,  and  is  called  the  center  of  curvature.  G 
is  the  vertex  of  the  mirror.  A  straight  line,  D  G,  drawn  through 

the  center  of  the  cur- 
vature and  the  vertex 
is  called  the  principal 
-D  axis  of  the  mirror.  A 
concave  mirror  may  be 
considered  as  made  up 
of  an  infinite  number 
of  small  plane  surfaces. 

All  radii  of  the  mirror,  as  C  A,  C  G,  and  C  B,  are  perpendicular 
to  the  small  planes  which  they  strike.  If  C  be  a  luminous 
point,  it  is  evident  that  all  light-waves  emanating  from  this 
point,  and  striking  the  mirror,  will  be  reflected  to  their  source 
at  C. 

Let  E  be  any  luminous  point  in  front  of  a  concave  mirror. 
To  find  the  direction  that  rays  emanating  from  this  point 
take  after  reflection,  draw  any  two  lines  from  this  point,  as 
E  A  and  E  B,  representing  two  of  the  infinite  number  of  rays 
composing  the  divergent  pencil  that  strike  the  mirror.  Next, 
draw  radii  to  the  points  of  incidence  A  and  B,  and  draw  the 
lines  A  F  and  B  F,  making  the  angles  of  reflection  equal  to 
the  angles  of  incidence.  Place  arrow  heads  on  the  lines  rep- 
resenting rays  to  indicate  the  direction  of  the  motion.  The 
lines  A  F  and  B  F  represent  the  direction  of  the  rays  after 
reflection. 

It  will  be  seen  that  the  rays  after  reflection  are  convergent, 
and  meet  at  the  point  F,  called  the  focus.  This  point  is  the 
focus  of  reflected  rays  that  emanate  from  the  point  E.  It 
is  obvious  that  if  F  were  the  luminous  point,  the  lines  A  E 
and  B  E  would  represent  the  reflected  rays,  and  E  would  be 
the  focus  of  these  rays.  Since  the  relation  between  the  two 
points  is  such  that  light-waves  emanating  from  either  one  are 


REFLECTION    FROM   MIRRORS.  221 

brought  by  reflection  to  a  focus  at  the  other,  these  points  are 
called  conjugate  foci.  Conjugate  foci  are  two  points  so  related 
that  the  image  of  either  is  formed  at  the  other.  The  rays  E  A 
and  E  B,  emanating  from  E,  are  less  divergent  £han  rays  F  A 
and  F  B,  emanating  from  a  point,  F,  less  distant  from  the 
mirror,  and  striking  the  same  points.  K-ays  M 

emanating   from  D,  and  striking   the    same        /  _ 
points  A  and  B,  will  be  still  less  divergent  ;       /x>-^p 
and  if  the  point  D  were  removed  to  a  distance     ^^^E—I^-\4 
of  many  miles,  the  rays   incident  at  these       \ 
points  would  be  very  nearly  parallel.    Hence, 
rays  may  be  regarded  as  practically  parallel 
when  their  source  is  at  a  very  great  distance,  e.g.  the  sun's 
rays.      If   a   sunbeam,    consisting   of   a   bundle   of    parallel 
rays,  as  E  A,  D  G,  and  H  B  (Fig.  175),  strike  a  concave  mirror 
in  a  direction  parallel  to  its  principal  axis,  these  rays  become 
convergent  by  reflection,  and  meet  at  a  point  (F)  in  the  principal 
axis.     This  point,  called  the  principal  focus,1  is  about  halfway 
between  the  center  of  curvature  and  the  vertex  of  the  mirror. 

On  the  other  hand,  it  is  obvious  that  divergent  rays  emanat- 
ing from  the  principal  focus  of  a  concave  mirror  become  parallel 
by  reflection, 

The  general  effect  of  a  concave  mirror  is  to  increase  the  con- 
vergence or  to  decrease  the  divergence  of  incident  rays. 

The  following  is  a  formula  for  concave  mirrors  : 


,  1 

P       P        f 

in  which  /represents  the  distance  of  the  principal  focus  from 
the  mirror,  and  p  and  p'  represent  the  respective  distances  of 
any  two  conjugate  foci  from  the  mirror.  Evidently,  if  any 

1  The  statement  that  parallel  rays,  after  reflection  from  a  concave  mirror,  meet  at 
the  principal  focus,  is  only  approximately  true.  The  smaller  the  angle  subtended 
at  the  center  by  the  mirror,  the  more  nearly  true  is  the  statement.  It  is  strictly 
true  only  of  parabolic  mirrors.  Such  are  used  in  the  headlights  of  locomotives. 


222  ETHEft    DYNAMICS. 

two  of  the  three  quantities  involved  be  given,  the  third  may 
be  calculated.  If  p  and  p'  have  unlike  signs,  we  are  to  under- 
stand that  the  object  and  the  image  are  on  opposite  sides  of 
the  mirror  ;  in  other  words,  the  image  is  virtual. 

231.  Formation  of  Images.  To  determine  the  position  and 
kind  of  images  formed  in  concave  mirrors,  of  objects  placed  in 
front  of  them,  proceed  as  follows  :  Locate  the  object,  as  D  E 
(Fig.  176).  Draw  lines,  E  A  and  D  B,  from  the  extremities  of 
the  object  through  the  center  of  curvature  of  the  mirror,  to 

meet  the  mirror.  These  lines  are 
called  secondary  axes.  Incident  rays 
along  these  lines  will  return  by  the 
same  paths  after  reflection.  Draw 
another  line  from  D  to  any  point  in 
the  mirror,  e.g.  to  F,  to  represent 
another  of  the  infinite  number  of 
rays  emanating  from  D.  Make  the 
angle  of  reflection  C  F  D'  equal  to 

the  angle  of  incidence  C  F  D,  and  the  reflected  ray  will  inter- 
sect the  secondary  axis  D  B  at  the  point  D'.  This  point  is  the 
conjugate  focus  of  all  rays  proceeding  from  D.  Consequently, 
an  image  of  the  point  D  is  formed  at  D'.  This  image  is  called 
a  real  image,  because  rays  actually  meet  at  this  point.  In  a 
similar  manner,  find  the  point  E',  the  conjugate  focus  of  the 
point  E.  The  Images  of  intermediate  points  between  D  and  E 
lie  between  the  points  D'  and  E';  and,  consequently,  the  image 
of  the  object  lies  between  those  points  as  extremities. 

It  thus  appears  that  an  image  of  an  object  placed  beyond  the 
center  of  curvature  of  a  concave  mirror  is  real,  inverted,  smaller 
than  the  object,  and  located  between  the  center  of  curvature  and 
the  principal  focus  of  the  mirror.  A  person  standing  in  front 
of  such  a  mirror,  at  a  distance  greater  than  its  radius  of 
curvature,  will  see  an  inverted  image  of  himself  suspended, 
as  it  were,  in  mid-air. 


FORMATION   OF   IMAGES. 


223 


FIG.  177. 


Experiment  3.     Hold  some  object,  e.g.  a  rose,  as  a  b  (Fig.  177),  a 
few  feet  in  front  of  a  concave  mirror.     Looking  in  the  direction  of  the 
axis  of  the  mirror,  you 
see    a   small    inverted 
image,  A  B,  of  the  ob- 
ject, between  the  center      ^§^     ^X.  b. 
of  curvature,  C,  of  the 
mirror  and  its  principal 
focus,  F. 

Figure  178  shows  the 
path  of  rays  thus  re- 
flected as  they  enter  the 
eye.  The  observer  sees 
the  image  of  the  point 
A  at  A'. 

Evidently,     if     A  B 
(Fig.  177)  represent  an  object  placed  between  the  principal  focus  and  the 
center  of  curvature,  then  a  b  will  represent  the  image  of  the  object. 

Hence,  the  image  of  an  object  placed  between  the  principal 

focus  and  the  center  of  curva- 
ture is  also  real  and  inverted,  but 
larger  than  the  object,  and  located 
beyond  the  center  of  curvature. 
The  image  in  this  case  may  be 
projected  upon  a  screen,  but 
it  will  not  be  so  bright  as  in 

the  former  case,  because  the  light  is.  spread   over -a  larger 

surface. 

Construct  an  image  of  an  object 

placed  between  the  principal  focus 

and  the  mirror,  as  in  Fig.  179.     It 

will   be   seen   in  this  case  that  a 

pencil  of  rays  proceeding  from  any 

point  of  an   object,   e.g.  A,  has  no 

actual  focus,  but  appears  to  proceed 

from  a  virtual  focus  A',  back  of  the  mirror,  and  so  with  other 

points,  as  B.      The  image  of  an  object  placed  between  the  prin- 


FlG.  178. 


FIG.  179. 


224  ETHER    DYNAMICS. 

cipal  focus  and  the  mirror  is  virtual,  erect,  larger   than    the 
object,  and  back  of  the  mirror. 

The  diagram  in  Fig.  180  suggests  the 
method  of  finding  the  disposition  of  a 
P     pencil  of  rays  emanating  from  any  point 
(e.fj.  A)   after   reflection  from  a  convex 
mirror.     Construct  an  image  of  an  object 
FIG.  iso.  placed  in  front  of  a  convex  mirror. 

EXERCISES. 

1.  With  a  radius  of  8  cm.  draw  arcs  of  circles  to  represent  concave 
mirrors,  draw  their  principal  axes,  and  locate  thereon  by  the-  letters  C  and 
F,  respectively,  the  centers  of  curvature  and  principal  foci.     Construct 
images  of  arrows  located  as  follows  :    (a)  between  the  mirror  and  the 
principal  focus  ;  (6)  between  the  principal  focus  and  the  center  of  curva- 
ture ;  (c)  beyond  the  center  of  curvature. 

2.  An  object  is  10  feet  from  a  concave  mirror  ;  a  distinct  image  of  the 
object  is  formed  2  feet  from  the  mirror,     (a)  What  is  the  focal  length  of 
the  mirror  ?     (6)   Describe  the  image. 

3.  The  focal  length  of  a  concave  mirror  is  16  inches.     At  what  dis- 
tance from  the  mirror  will  the  image  of  an  object  which  is  18  inches 
from  the  mirror  appear  ? 

4.  Locate  and  describe  the  image,  if  the  object  in  Exercise  3  be  placed 
12  inches  from  the  mirror. 


SECTION   VI. 
REFRACTION. 

232.  Introductory  Experiments. 

Experiment  1.  Into  a  darkened  room  admit  a  sunbeam  so  that  its 
rays  may  fall  obliquely  on  the  bottom  of  the  basin  (Fig.  181),  and  note 
the  place  on  the  bottom  where  the  edge  of  the  shadow  D  E  cast  by  the 
side  of  the  basin  D  C  meets  the  bottom  at  E.  Then,  without  moving  the 
basin,  fill  it  evenly  full  with  water  slightly  clouded  with  milk  or  with  a 
few  drops  of  a  solution  of  mastic  in  alcohol.  It  will  be  found  that  the 
edge  of  the  shadow  has  moved  from  D  E  to  D  F,  and  meets  the  bottom  at 
F.  Beat  a  blackboard  eraser,  and  create  a  cloud  of  dust  in  the  path  of 


EXPERIMENTS. 


225 


C 

B  ~E 

F 

N 

FIG.  181. 

the  beam  in  the  air,  and  you  will  discover  that  the  rays  G  D  that  graze 

the  edge  of  the  basin  at  D  become  bent  at  the  point  where  they  enter  the 

water,  and  now  move  in  the  bent  line 

G  D  F,  instead  of,  as  formerly,  in  the 

straight  line  G  D  E.     The  path  of  the 

line  in  the  water  is  now  nearer  to  the 

vertical  side  D  C  ;  in  other  words,  this 

part  of  the  beam  is  more  nearly  vertical 

than  before. 

Experiment  2.  Place  a  coin,  A 
(Fig.  182),  on  the  bottom  of  an  empty 
basin,  so  that,  as  you  look  over  the 
edge  of  the  vessel  through  a  small  hole 
in  a  card,  B  C,  the  coin  is  just  out  of 
sight.  Then,  without  moving  the  card 
or  basin,  fill  the  latter  with  water.  Now,  on  looking  through  the  aper- 
ture in  the  card,  you  find  that  the  coin  is  visible.  The  beam  A  E,  which 
formerly  moved  in  the  straight  line  A  D,  is 
now  bent  at  E,  where  it  leaves  the  water,  and, 
passing  through  the  aperture  in  the  card,  enters 
the  eye.  Observe  that  as  the  beam  passes  from 
the  water  into  the  air  it  is  turned  farther  from 
a  vertical  line,  E  F ;  in  other  words,  the  beam 
is  farther  from  the  vertical  than  before. 

Experiment  3.     Thrust  a  pencil  obliquely 
into  water  ;  it  will  appear  shortened,  and  bent 
at  the  surface  of  the  water,  and  the  immersed  portion  will  appear  elevated. 

Experiment  4.     Place  a  piece  of  wire  (Fig.  183)  vertically 
in  front  of  the  eye,  and  hold  a  narrow  strip  of  thick  plate  glass 
horizontally  across  the  wire,  so  that  the  light-waves  from  the 
wire  may  pass  obliquely  through  the  glass  to  the  eye.     The 
wire  will  appear  to  be  broken  at  the  two  edges  of  the  glass, 
and  the  intervening  section  will  appear  to  the  right  or  the  left 
according  to  the  inclination  of  the  glass  ;  but  if  the  glass  be  FlG<  183> 
not  inclined  to  the  one  side  or  the  other,  the  wire  does  not  appear 
broken. 

When  a  ray  of  light  passes  from  one  medium  into  another  of 
different  optical  density,  it  is  bent  or  refracted  at  the  interface 
between  the  two  mediums,  unless  it  meet  this  plane  perpen- 
dicularly. In  the  latter  case  there  is  no  refraction.  If  it 


FIG.  182. 


226 


ETHER   DYNAMICS. 


pass  into  a  denser  medium,  it  is  refracted  toward  the  perpen- 
dicular to  this  plane  ;  if  into  a  rarer  medium,  it  is  refracted 
from  the  perpendicular.  It  is  not  universally  true  that  the 
denser  mediums  are,  the  more  highly  refracting.  The  refrac- 
tive power  of  water  is  less  than  that  of  alcohol  or  of  oil  of 
turpentine.  A  substance  which  has  a  higher  refractive  power 
than  another  is  said  to  be  optically  denser. 

The  angle  G  D  0  (Fig.  181)  is  called  the  angle  of  incidence  ; 
F  D  N,  the  angle  of  refraction  ;  and  EOF,  the  angle  of  deviation. 

233.  Cause  of  Refraction.  Foucault  and  others  have 
proved  by  careful  experiments  that  the  speed  of  light  is  less 
in  water  than  in  air.  It  is  less  in  glass  than  in  water,  and 
much  less  in  diamond  than  in  glass.  Every  transparent  sub- 
stance has  its  own  rate  of  transmission.  It  would  seem  that 
there  is  an  interaction  between  the  ether  and  the  molecules 
of  matter  such  that  in  different  mediums  the  ether-waves  are 
unequally  retarded. 

Let  the  series  of  parallel  lines  A  B  (Fig.  184)  represent  a  series  of  wave- 
fronts  leaving  an  object,  C,  and  passing 
through  a  rectangular  piece  of  glass,  D  E, 
and  constituting  a  beam.  Every  point 
in  a  wave-front  moves  with  equal  velocity 
as  long  as  it  traverses  the  same  medium  ; 
but  the  point  a  of  a  given  wave-front,  a  b, 
enters  the  glass  first,  and  its  velocity  is  im- 
peded, while  the  point  b  retains  its  original 
velocity  ;  so  that,  while  the  point  a  moves 
to  a',  b  moves  to  b',  and  the  result  is 
that  the  wave-front  assumes  a  new  direc- 
tion  (very  much  in  the  same  manner  as 
a  line  of  soldiers  executes  a  wheel),  and 
a  ray  or  a  line  drawn  perpendicularly 
through  the  series  of  waves  is  turned  out 

of  its  original  direction  on  entering  the  glass.  Again,  the  extremity  c  of 
a  given  wave-front,  c  d,  first  emerges  from  the  glass,  when  its  velocity  is 
immediately  quickened  ;  so  that  while  d  advances  to  d',  c  advances  to  c', 


INDEX    OF    REFRACTION. 


227 


and  the  direction  of  the  ray  is  again  changed.  The  direction  of  the  ray 
after  emerging  from  the  glass  is  parallel  to  its  direction  before  entering 
it,  but  it  has  suffered  a  lateral  displacement. 

It  is  evident  that  if  the  ray  enter  the  new  medium  in  a  direction  per- 
pendicular to  its  surface,  i.e.  with  its  wave-front  parallel  to  this  surface, 
all  parts  of  the  wave-front  will  be  retarded  simultaneously  and  no 
refraction  will  take  place. 

234.  Index  of  Refraction.  The  deviation  of  light-waves  in 
passing  from  one  medium  into  another  depends  upon  the 
optical  density  of  the  mediums  and  the  angle  of  incidence. 
It  diminishes  as  the  angle 
of  incidence  diminishes, 
and  is  zero  when  the  inci- 
dent ray  is  normal.  It  is 
highly  important,  when 
the  angle  of  incidence  is 
known,  to  be  able  to  deter- 
mine the  direction  which 
a  ray  will  take  on  entering 
a  new  medium.  Describe 
a  circle  around  the  point 
of  incidence  A  (Fig.  185) 
as  a  center  ;  through  the 
same  point  draw  I  H  perpendicular  to  the  surfaces  of  the  two 
mediums,  and  to  this  line  drop  perpendiculars  B  D  and  C  E 
from  the  points  where  the  circle  cuts  the  ray  in  the  two 
mediums.  Then  suppose  that  the  perpendicular  B  D  is  T%  of 
the  radius  A  B. ;  now,  this  fraction  T8¥  is  called  the  sine  of  the 
angle  DAB.  Hence,  T8^  is  the  sine  of  the  angle  of  incidence. 
Again,  if  we  suppose  that  the  perpendicular  C  E  is  T6^  of  the 
radius,  then  the  fraction  ^  is  the  sine  of  the  angle  of  refrac- 
tion. The  sines  of  the  two  angles  are  to  each  other  as  T%  :  T6W, 
or  as  4  :  3.  The  quotient  (in  this  case  £  =1.33  +)  obtained 
by  dividing  the  sine  of  the  angle  of  incidence  by  the  sine 
of  the  angle  of  refraction  (generally  expressed  decimally) 


FIG.  iss. 


228  ETHER,    DYNAMICS. 

is  called  the  index  of  refraction.  The  incident  ray  may  be 
more  or  less  oblique,  yet  the  quotient  (i.e.  the  index  of  refrac- 
tion) remains  the  same. 

235.  Indices  of  Refraction.  The  index  of  refraction  for 
light-waves  in  passing  from  air  into  water  is  approximately  |, 
and  from  air  into  glass,  f ;  of  course,  if  the  order  be  reversed, 
the  reciprocal  of  these  fractions  must  be  taken  as  the  indices ; 
e.g.  from  water  into  air  the  index  is  f ;  from  glass  into  air,  f . 
When  a  ray  passes  from  a  vacuum  into  a  medium,  the  refrac- 
tive index  is  greater  than  unity,  and  is  called  the  absolute 
index  of  refraction.  The  relative  index  of  refraction,  from  any 
medium,  A,  into  another,  B,  is  found  by  dividing  the  absolute 
index  of  B  by  the  absolute  index  of  A. 

The  refractive  index  varies  with  wave-length.  The  following  table  is 
intended  to  represent  mean  indices  for  light- waves : 

TABLE    OF    ABSOLUTE    INDICES. 


Lead  chromate 2.97 

Diamond  (about)    .     .     .     .  2.5 

Carbon  disulphide  .     .     .     .  1.64 

Flint  glass  (about) ....  1.61 

Agate 1.54 

Canada  balsam  .     .     .     ...  1.53 

Crown  glass  (about)    .     .     .1.53 


Spirits  of  turpentine  .     .     1.48 

Alcohol 1.37 

Humors  of  the  eye  (about)  1.35 

Pure  water 1.33 

Air  at  0°  C.  and  760  mm. 

pressure 1.000294 


236.  Critical  Angle ;  Total  Reflection.  Let  SS'  (Fig.  186) 
represent  the  boundary  surface  between  two  mediums,  and 
AO  and  BO  incident  rays  in  the  more  refractive  medium 
(e.g.  glass)  ;  then  O  D  and  O  E  may  represent  the  same  rays, 
respectively,  after  they  enter  the  less  refractive  medium  (e.g. 
air).  It  will  be  seen  that,  as  the  angle  of  incidence  is  in- 
creased, the  refracted  ray  rapidly  approaches  the  surface  0  S. 
Now,  there  must  be  an  angle  of  incidence  (e.g.  COM)  such 
that  the  angle  of  refraction  will  be  90°;  in  this  case  the 


REFRACTION   AND    TOTAL    REFLECTION. 


229 


incident  ray  C  0,  after  refraction,  will  just  graze  the  surface 
0  S.  This  angle  (C  0  M),  which  must  not  be  exceeded  if  the  ray 
is  to  pass  out  into  the  air,  is  called  the  critical  or  limiting  angle. 
Any  incident  ray,  making  a  larger  angle  with  the  normal  than 
the  critical  angle,  as  LO,  cannot  emerge  from  the  medium, 
and  consequently  is  not  refracted.  Experiment  shows  that 


FIG. 186. 


all  such  rays  undergo  internal  reflection  ;  e.g.  the  ray  LO  is 
reflected  in  the  direction  O  N.  Reflection  in  this  case  is  so 
nearly  perfect  that  it  has  received  the  special  name  total 
reflection.  Total  reflection  occurs  when  rays  in  the  more 
refractive  medium  are  incident  at  an  angle  greater  than  the 
critical  angle. 

Surfaces  of  transparent  mediums,  under  these  circumstances,  consti- 
tute the  best  mirrors  possible.  The  critical  angle  diminishes  as  the 
refractive  index  increases.  For  water  it  is  about  48-£°  ;  for  flint  glass, 
38°  41' ;  and  for  the  diamond,  23°  41'.  Light-waves  cannot,  therefore, 
pass  out  of  water  into  air  with  a  greater  angle  of  incidence  than  48£°. 
The  brilliancy  of  gems,  particularly  of  the  diamond,  is  due  in  part  to 
their  extraordinary  power  of  reflection,  arising  from  their  large  indices 
of  refraction  or  the  smallness  of  their  critical  angles. 


230 


ETHER    DYNAMICS. 


237.  Illustrations  of  Refraction  and  Total  Reflection. 

Experiment  5.  Observe  the  image  of  a  candle  flame  reflected  by  the 
surface  of  water  in  a  glass  beaker,  as  in  Fig.  187. 

Experiment  6.  Thrust  the  closed  end  of  a  glass  test-tube  (Fig.  188) 
into  water  and  incline  the  tube.  Look  down  upon  the  immersed  part 


FIG.  187. 


FIG.  188. 


A'* 


FIG. 


H 


of  the  tube,  and  its  upper  surface  will  look  like  burnished  silver,  or  as  if 
the  tube  contained  mercury.     Fill  the  test-tube  with  water,  and  immerse 

as  before  ;  the  total  reflection  which 
before  occurred  at  the  surface  of  the 
air  in  the  submerged  tube  now  dis- 
appears. Explain. 

A  ray  of  light  from  a  heavenly 
body,  A  (Fig.  189),  undergoes  a  series 
of  refractions  as  it  reaches  successive 
strata  of  the  atmosphere  of  constantly 
increasing  density,  and  to  an  eye  at 
the  earth's  surface  appears  to  come 
from  a  point,  A',  in  the  heavens.  The 
general  effect  of  the  atmosphere  on 
the  path  of  light  that  traverses  it  is 
such  as  to  increase  the  apparent  alti- 
tude of  the  heavenly  bodies.  It  enables  us  to  see  a  body,  B,  which  is 
actually  below  the  horizon  H  H,  and  prolongs  the  apparent  stay  of  the 
sun,  moon,  and  other  heavenly  bodies,  above  the  horizon.  Twilight  is 
due  to  both  refraction  and  reflection  of  light  by  the  atmosphere. 


OPTICAL    PRISMS. 


231 


SECTION   VII. 
PRISMS   AND   LENSES. 

238,  Optical  Prisms.     An  optical  prism  is  a  portion  of  a 
transparent  medium  bounded  by  two  plane  surfaces  inclined 
to  each  other.     Fig.  190  represents  a  transverse  section  of  a 
common  form  of  prism.     Let  A  B 

be  a  ray  of  light  incident  upon 
one  of  its  surfaces.  On  entering 
the  prism  it  is  refracted  toward 
the  normal,  and  takes  the  direc- 
tion B  C.  On  emerging  from  the 
prism  it  is  again  refracted,  but 
now  from  the  normal  in  the  direc- 
tion C  D.  The  object  that  emits  the  ray  will  appear  in  the 
direction  D  E  F.  Observe  that  the  ray  A  B,  at  both  refractions, 
is  bent  toward  the  thicker  part,  or  base,  of  the  prism. 

239.  Lenses.     Any  transparent  medium  bounded  by  sur- 

faces of  which  at 
least  one  is  curved, 
is  a  lens. 

Lenses  are  of  two 
classes,  converging 
and  diverging,  ac- 
cording as  they  collect  rays  or  cause  them  to  diverge.  Each 
class  comprises  three  kinds  (Fig.  191)  : 


FIG.  190. 


—A 


FIG.  191. 


1.  Bi-convex 


CLASS  I. 

Converging, 


^1 


2.  Plano-convex 

3.  Concavo-convex  f 

(or  meniscus)  J 


convex  lenses, 
thicker  in  the 
middle  than  at 
the  edges. 


CLASS  II. 

4.  Bi-concave        )  Diverging,  or  con- 

5.  Plano-concave- 1     cave  lenses,  thin- 

6.  Convexo-con-    j     ner  in  the  middle 

cave  j     than  at  the  edges. 


A  straight  line  normal  to  both  surfaces  of  a  lens  and  pass- 
ing through  their  centers  of  curvature,  as  A  B,  is  called  its 
principal  axis.  There  is  a  point  in  the  principal  axis  of  every 


232 


ETHER    DYNAMICS. 


FIG.  192. 


lens,  either  at  or  near  its  center  of  volume,  called  its  optical 
center,  so  placed  that  rays  of  light  which  pass  through  this 
point  and  the  lens  suffer  no  change  of  direction,  though  there 
may  be  a  slight  lateral  displacement.  In  lenses  1  and  4  it  is 
halfway  between  their  respective  curved  surfaces. 

240.  Effect  of  Lenses.  The  general  effect  of  all  convex  lenses 
is  to  cause  transmitted  rays  to  converge  ;  that  of  concave  lenses, 

to  cause  them  to  diverge.  In- 
cident rays  parallel  to  the 
principal  axis  of  a  convex 
lens  are  brought  to  a  focus,  F 
(Fig.  192),  at  a  point  in  the 
principal  axis.  This  point 
is  called  the  principal  focus,  i.e.  it  is  the  focus  of  incident 
rays  parallel  to  the  principal  axis.  It  may  be  found  by  hold- 
ing the  lens  so  that  the  rays  of  the  sun  may  fall  perpendicu- 
larly upon  it,  and  then  moving  a  sheet  of  paper  back  and 
forth  behind  it  until  the  image  of  the  sun  formed  on  the 
paper  is  brightest 
and  smallest.  The 
focal  length  is  the 
distance  from  the 
optical  center  of 
the  lens  to  the  cen- 
ter of  the  image 
on  the  paper.  The 
shorter  the  focal  length  the  more  powerful  is  the  lens  ;  that  is, 
the  more  quickly  are  the  parallel  rays  that  traverse  different 
parts  of  the  lens  brought  to  cross  one  another. 

A  pencil  of  rays,  emitted  from  the  principal  focus  F  (Fig.  192) 
as  a  luminous  point,  becomes  parallel  on  emerging  from  a  convex 
lens.  If  the  rays  emanate  from  a  point  nearer  the  lens,  they 
diverge  after  egress,  but  the  divergence  is  less  than  before  ;  if 
from  a  point  beyond  the  principal  focus,  the  rays  are  rendered 


193. 


CONJUGATE   FOCI.  233 

convergent.  A  concave  lens  causes  parallel  incident  rays  to 
diverge  as  if  they  came  from  a  point,  as  F  (Fig.  193).  This 
point  is  therefore  its  principal  focus.  It  is,  of  course,  a 
virtual  focus. 

Every  lens  has  a  principal  focus  ;  it  is  the  point  to  which 
parallel  rays  are  caused  to  converge,  or  from  which,  after 
deflection,  they  appear  to  diverge,  as  the  case  may  be. 

241.  Conjugate  Foci.     When  a  luminous  point,  S,  beyond 
the  principal  focus  (Fig.  194)  sends  rays  to  a  convex  lens,  the 
emergent    rays 

converge  to  an- 
other point,  S' ; 
rays  sent  from 

S'  to   the   lens 

i  i  FIG.  194 

would  converge 

to  S.  Two  points  thus  related  are  called  conjugate  foci.  The 
fact  that  rays  which  emanate  from  one  point  are  caused  by 
convex  lenses  to  collect  at  one  point,  gives  rise  to  real  images, 
as  in  the  case  of  concave  mirrors. 

242.  Law  of  Converging  Lenses. 

Lenses,  like  mirrors,  have  conjugate  foci  at  distances  p  and 
p'  from  the  optical  centers.  In  converging  lenses  the  prin- 
cipal focal  distance  and  the  distance  of  their  conjugate  foci 
(or  distance  of  object  and  image)  are  related  according  to  the 
formula 

1+1  =  1. 

p  P'  f 

Hence,  the  law  of  converging  lenses  :  The  reciprocal  of  the 
principal  focal  length  is  equal  to  the  sum  of  the  reciprocals  of 
any  two  conjugate  focal  lengths. 

When  a  pencil  of  light  comes  from  an  infinite  distance  (i.e.  when  its 
rays  are  parallel),  p  =•  co  ;  then  p'  =/,  and  the  rays  converge  at  the  prin- 
cipal focus.  Conversely,  if  a  pencil  come  from  the  principal  focus, 
p=f;  hence  p'  =  GO  ;  that  is,  no  image  is  formed. 


234 


ETHE£  DYNAMICS. 


If  the  object  (i.e.  the  source  of  light)  be  at  a  distance  less  than  infinity, 
but  greater  than  2/,  the  image  is  real,  and  is  on  the  other  side  of  the 
lens  at  a  distance  greater  than  /and  less  than  2/.  Conversely,  if  the 
object  be  at  a  distance  greater  than  /,  but  less  than  2/,  the  image  is  at  a 
distance  greater  than  2/. 

243,  Images  Formed.  Fairly  distinct  images  of  objects 
may  be  formed  through  very  small  apertures  (§  220)  ;  but 
owing  to  the  small  quantity  of  light  that  passes  through  the 
aperture,  the  images  are  very  deficient  in  brilliancy.  If  the 
aperture  be  enlarged,  brilliancy  is  increased  at  the  expense  of 
distinctness.  A  convex  lens  enables  us  to  obtain  both  brilliancy 
and  distinctness  at  the  same  time. 

Experiment.  By  means  of  a  porte-lumiere,  A  (Fig.  195),  introduce 
a  horizontal  beam  of  light  into  a  darkened  room.  In  its  path  place  some 
object,  as  B,  painted  in  transparent  colors  or  photographed  on  glass. 
(Transparent  pictures  are  cheaply  prepared  by  photographers  for  sunlight 
and  lime-light  projections.)  Beyond  the  object  place  a  convex  lens,  L, 
and  beyond  the  lens  a  screen,  S  S.  The  object  being  illuminated  by  the 
beam  of  light,  all  the  rays  diverging  fr6m  any  point,  a,  are  bent  by  the 


S    S      S' 


FIG.  195. 


lens  so  as  to  come  together  at  the  point  a'.  In  like  manner,  all  the  rays 
proceeding  from  C  are  brought  to  the  same  point  C';  and  so  also  for  all 
intermediate  points.  Thus,  out  of  the  numberless  rays  emanating  from 
each  of  the  points  on  the  object,  those  that  reach  the  lens  are  guided  by 
it,  each  to  its  own  appropriate  point  in  the  image.  It  is  evident  that 
there  must  result  an  image  both  bright  and  distinct,  provided  the  screen 


CONSTRUCTION   OF   IMAGES. 


235 


be  suitably  placed,  i.e.  at  the  place  where  the  rays  meet.  But  if  the 
screen  be  placed  at  S'  S'  or  S"  S",  it  is  evident  that  a  blurred  image  will 
be  formed.  Instead  of  moving  the  screen 
back  and  forth,  in  order  to  "  focus  "  the 
rays  properly,  it  is  customary  to  move 
the  lens. 

Figure  196  shows  more  accurately  the 
form  of  the  image  produced  by  the  ordi- 
nary convex  lens.  It  is  apparent  that  if 
the  center  of  the  image  A"  B'  be  properly 
focused  upon  a  screen  the  extremities  of  the  image  will  be  a  little  out  of 
focus,  and  vice  versa. 

244.  Construction   of   Images  Formed  by  Convex  Lenses. 

Given  the  lens  L  (Fig.  197),  whose  principal  focus  is  at  F, 
and  object  A  B  in  front  of  it ;  any  two  of  the  many  rays  from 
A  will  determine  where  its  image  a  is  formed.  Two  rays  that 
can  be  traced  easily  are,  one  along  the  secondary  axis  A  0  a, 


FIG.  196. 


FIG.  197. 

and  one  A  A'  parallel  to  the  principal  axis  ;  the  latter  will  be 
deviated  so  as  to  pass  through  the  principal  focus  F,  and 
will  afterward  intersect  the  secondary  axis  at  some  point,  a  ; 
therefore  this  is  the  conjugate  focus  of  A.  Kays  can  be 
similarly  traced  for  B  and  all  intermediate  points  along  the 
arrow.  Thus,  a  real  inverted  image  is  formed  at  a  b. 

The  linear  dimensions  of  an  object  and  of  its  image  formed 
by  a  convex  lens  are  proportional  to  their  respective  distances 
from  the  center  of  the  lens. 

245,  Virtual  Images.  Since  rays  that  emanate  from  a 
point  nearer  the  lens  than  the  principal  focus  diverge  after 


236 


ETHER    DYNAMICS. 


egress,  it  is  evident  that  their  focus  must  be  virtual  and  on 
the  same  side  of  the  lens  as  the  object.  Hence,  the  image  of 
an  object  placed  nearer  the  lens  than  the  principal  focus  is. 
virtual,  magnified,  and  erect,  as  shown  in  Fig.  198.  A  convex 
lens  used  in  this  manner  is  called  a  simple  microscope. 

246.  Simple  Microscope.  As  its  name  implies,  the  micro- 
scope is  an  instrument  for  viewing  minute  objects.  The 
simple  microscope  consists  of  a  single  converging  lens  so 
placed  that  the  object  is  between  the  principal  focus  and  the 
lens.  It  magnifies  b  increasing  the  visual  angle. 


A' 


FIG.  198. 

The  magnifying  power  of  the  lens  is  simply  the  ratio 
between  the  apparent  linear  dimension  of  the  image  and  the 
corresponding  dimension  of  the  object,  e.g.  A'  B' :  A  B  (Fig.  198), 
or  it  is  the  ratio  between  the  visual  angles  under  which  the 
eye  would  see  image  and  object,  if  both  were  placed  at  the 
distance  of  distinct  vision.1  If  the  lens  be  of  short  focus,  as 
is  usually  the  case,  the  magnifying  power  is  approximately 
the  ratio  of  the  distance  of  distinct  vision  to  the  focal  length. 
Thus  a  lens  of  -J-  inch  focal  length  would  magnify  20  to  24 
times. 

1  For  normal  eyes,  an  object  to  be  seen  most  distinctly  must  be  placed  at  a  distance 
of  10  to  12  inches  ;  hence  this  is  regarded  as  the  distance  of  distinct  vision. 


SPHERICAL    ABERRATION. 


237 


247.  Diverging  Lenses.  Since  the  effect  of  concave  lenses 
is  to  render  transmitted  rays  divergent,  pencils  of  rays 
emitted  from  A  and  B  (Fig.  199)  diverge  after  refraction,  as 
if  they  came  from  A'  and  B',  and  the  image  appears  to  be  at 
A'  B'.  Hence,  images  formed  by  concave  lenses  are  virtual, 
erect)  and  smaller  than  the  object. 


FIG.  199. 

248,  Spherical  Aberration.  In  all  ordinary  convex  lenses 
the  curved  surfaces  are  spherical,  and  the  angles  which  inci- 
dent rays  make  with  the  little  plane  surfaces,  of  which  we 
may  imagine  the  spherical  surface  to  be  made  up,  increase 
rapidly  toward  the  edge  of  the  lens.  Thus,  while  those  rays 


from  a  given  point  of  an  object  which  pass  through  the  cen- 
tral portion  (Fig.  200)  meet  approximately  at  the  same 
point  F,  those  which  pass  through  the  marginal  portion 
are  deflected  so  much  that  they  cross  the  axis  at  nearer  points, 
e.g.  at  F ;  so  a  blurred  image  results.  This  wandering  of  the 
rays  from  a  single  focus  is  called  spherical  aberration. 

N"o  lens  with  spherical  surfaces  can  bring  all  the  rays  to 
the  same  focus.  The  evil  may  be  in  a  measure  corrected  by 
interposing  a  diaphragm,  D  D',  provided  with  a  central  aperture 


238  ETHER   DYNAMICS. 

smaller  than  the  lens,  so  as  to  cut  off  those  rays  that  pass 
through  the  marginal  part  of  the  lens.  But  it  can  be  wholly 
corrected  only  by  properly  modifying  the  curvature  of  the 
surfaces  of  the  lens.  A  lens  having  surfaces  thus  modified  is 
said  to  be  aplanatic. 

EXERCISES. 

1.  What  must  be  the  position  of  an  object  with  reference  to  a  con- 
verging lens,  that  its  image  may  be  real  and  magnified  ? 

2.  A  photographic  transparency  is  placed  between  a  porte-lumiere 
and  a  bi-convex  lens,  16  inches  from  the  latter.     How  many  diameters 
is  a  distinct  image  of  the  transparency  multiplied  on  a  screen  20  feet 
distant  ? 

3.  A  transparency  whose  dimensions  are  3x4  inches  is  placed  16 
inches  from  the  lens.     At  what  distance  from  the  lens  must  the  screen  be 
that  it  may  receive  a  distinct  image  of  the  transparency  that  shall  cover 
a  surface  3x4  feet  ? 

4.  What  is  the  focal  length  of  the  lens  used  in  the  last  case  ? 

5.  With  a  converging  lens  the  image  of  a  candle  is  thrown  on  a 
screen  6  feet  from  the  candle,  and  the  focal  length  of  the  lens  is  16 
inches.     Find  the  distances  of  the  candle  and  of  the  screen  from  the 
lens. 

6.  A  luminous  point  is  3  inches  from  a  convex  lens  having  a  focal 
length  of  5  inches.     Find  the  position  of  the  image. 

7.  If  the  candle  and  the  screen  be  3  feet  apart,  and  the  lens  be  mid- 
way between  them,  what  is  the  focal  length  ? 

8.  Find  the  focal  length  of  a  lens  which  throws  the  image  of  an 
object  5  feet  distant  on  a  screen  3  feet  distant. 

9.  About  what  is  the  focal  length  of  a  simple  microscope  that  mag- 
nifies 30  times  ? 

10.  About  how  many  times  does  a  lens  of  2  inches  focal  length 
magnify  ? 

11.  (a)  What  is  meant  by  the  "power"  of  a  simple  microscope? 
(6)  What  is  necessary  that  it  may  have  great  power  ? 

12.  If  an  object  be  at  twice  the  focal  distance  of  a  convex  lens,  how 
will  the  length  of  the  image  compare  with  the  length  of  the  object  ? 

13.  To  an  eye  whose  distance  of  distinct  vision  is  25  cm.,  how  many 
diameters  will  a  lens  of  1  cm.  focus  magnify  ? 

14.  Show  that  a  concave  air  lens  in  water  has  the  same  effect  on  inci- 
dent light  as  a  convex  water  lens  in  air. 


ANALYSIS    OF    SUNLIGHT. 


239 


SECTION  vm. 

PRISMATIC    ANALYSIS   OF   LIGHT.      SPECTRUMS. 

249.  Analysis  of  Sunlight. 

Experiment  1.  Place  a  disk  with  an  adjustable  slit  in  the  aperture 
of  a  porte-lumiere  so  as  to  exclude  from  a  darkened  room  all  light-waves 
except  those  which  pass  through  the  slit.  Near  the  slit  interpose  a 
double-convex  lens  of  (say)  10-inch  focus.  A  narrow  sheet  of  light  will 
traverse  the  room  and  produce  an  image,  A  B  (Fig.  201),  of  the  slit  on  a 
white  screen  placed  in  its  path.  Now  place  a  glass  prism,  C,  in  the  path 


FIG.  201. 

of  the  narrow  sheet  of  light  and  near  to  the  lens,  with  its  edge  vertical. 
(1)  Not  only  is  the  light  now  turned  from  its  former  path,  but  that  which 
before  was  a  narrow  sheet  is,  after  emerging  from  the  prism,  spread  out 
fan-like  into  a  wedge-shaped  body,  with  its  thickest  part  resting  on  the 
screen.  (2)  The  image,  before  only  a  narrow,  vertical  band,  A  B,  is  now 
drawn  out  into  a  long  horizontal  ribbon,  D  E.  (3)  The  image,  before 
white,  now  presents  all  the  colors  of  the  rainbow,  from  red  at  one  end  to 
violet  at  the  other ;  it  passes  gradually  through  all  the  gradations  of 
orange,  yellow,  green,  blue,  and  violet.  (The  difference  in  deviation 
between  the  red  and  the  violet  is  purposely  much  exaggerated  in  the 
figure.) 


240  ETHER*  DYNAMICS. 

• 

From  this  experiment  we  learn  (1)  that  white  light  is  not 
simple  in  its  composition,  but  the  result  of  a  mixture  of  colors.1 
(2)  The  colors  of  which  white  light  is  composed  may  be  sepa- 
rated by  refraction.  (3)  The  separation  is  due  to  the  different 
degrees  of  deviation  which  colors  undergo  by  refraction.  Red, 
which  is  always  least  turned  aside  from  a  straight  path,  is 
the  least  refrangible  color.  Then  follow  orange,  yellow, 
green,  blue,  and  violet,  in  the  order  of  their  refrangibility. 
The  many-colored  ribbon  of  light  D  E  is  called  the  solar  spec^ 
trum.2  This  separation  of  white  light  into  its  constituents  is 
called  dispersion.  The  number  of  colors  of  which  white  light 
is  composed  is  really  infinite,  but  we  have  names  for  only 
seven  of  them  ;  viz.  red,  orange,  yellow,  green,  cyan-blue,  ultra- 
marine-blue, and  violet;  and  these  are  called  the  prismatic 
colors.  The  names  of  the  blues  are  derived  from  the  names 
of  the  pigments  which  most  closely  resemble  them. 

The  rainbow  is  a  solar  spectrum  on  a  grand  scale.  It  is  the 
result  of  refraction,  total  reflection,  and  dispersion  of  sunlight 
by  falling  raindrops. 

250,  Synthesis  of  White  Light.     The  composition  of  white 
light  has  been  ascertained  by  the  process  of  analysis  ;  it  can 
be  verified  by  synthesis ;  i.e.  the  colors  after  dispersion  may 
be  reunited,  and  the  result  of  the  reunion  is  white  light. 

Experiment  2.  Place  a  second  prism  (2)  in  such  a  position  AV tnat 
light  which  has  passed  through  one  prism  (1),  and  been  refracted  and 
decomposed,  may  be  refracted  back,  and  the  colors  will  be  reblended, 
and  a  white  image  of  the  slit  will  be  restored  on  the  screen. 

251,  Chromatic  Aberration.     There  is  in  ordinary  convex 
lenses  a  serious   defect,  to   which   we   have   not  before  re- 
ferred, called  chromatic  aberration,  the  correction  of  which  has 

1  Newton  (1666)  was  the  first  to  recognize  the  true  import  of  this  phenomenon,  i.e. 
to  refer  the  colors  to  the  heterogeneity  of  white  light. 

2  A  succession  of  colors  in  the  order  of  their  refrangibility,  obtained  from  uny 
source  of  light,  is  called  a  spectrum. 


CAUSE    OF    COLOR    AND    DISPERSION.  241 

demanded  the  highest  skill.  The  convex  lens  both  refracts  and 
disperses  the  light-waves  that  pass  through  it.  The  tendency, 
of  course,  is  to  bring  to  a  focus  the  more  refrangible  rays, 
as  the  violet,  much  sooner  than  the  less  refrangible  rays, 
such  as  the  red.  The  result  is  a  disagreeable  coloration  of 
the  images  that  are  formed  by  the  lens, 
especially  by  those  portions  of  the  light- 
waves that  pass  through  the  lens  near  its 
edges.  This  evil  may  be  overcome  very 
effectually  by  combining  with  the  convex  lens  a  plano-concave 
lens.  Now,  if  a  crown-glass  convex  lens  be  taken,  a  flint- 
glass  concave  lens  may  be  prepared  that  will  correct  the  dis- 
persion of  the  former  without  neutralizing  all  its  refraction.1 
A  compound  lens  composed  of  these  two  lenses  cemented 
together  (Fig.  202)  constitutes  what  is  called  an  achromatic 


252.  Cause  of  Color  and  Dispersion.  The  color  of  light  is 
determined  by  vibration-frequency,  or,  in  other  words,  by  the 
corresponding  wave-length.  The  light-waves  diminish  in 
length  from  the  red  to  the  violet.  As  pitch  depends  on 
the  frequency  with  which  aerial  waves  strike  the  ear,  so  color 
depends  upon  the  frequency  with  which  ether-waves  strike 
the  eye.  The  difference  between  violet  and  red  is  a  differ- 
ence analogous  to  the  difference  between  a  high  note  and  a 
low  note  on  a  piano. 

The  speed  of  propagation  in  a  vacuum  appears  to  be  the 
same  for  all  wave-lengths.  But  in  a  refracting  medium  the 
short  waves  are  more  retarded  than  the  longer  ones,  hence 
they  are  more  refracted.  This  is  the  cause  of  dispersion. 
Each  wave-length  has  its  own  refractive  index,  or,  since 
vibration-frequency  corresponds  to  color,  every  simple  color 
has  its  special  refractive  index.  Light  composed  of  waves  all 
of  the  same  (or  nearly  the  same)  length  is  called  homogeneous 

1  The  refractive  and  the  dispersive  powers  of  the  two  lenses  are  not  proportional. 


242  ETHER    DYNAMICS. 

or  monochromatic  light.  The  yellow  light  emitted  by  the 
flame  of  a  Bunsen  burner  or  alcohol  lamp  when  common  salt 
is  sifted  upon  it  is  approximately  monochromatic.  Ordinary 
white  light  is  a  mixture  of  long  and  short  ether-waves. 

From  well-established  data,  determined  by  a  variety  of  methods, 
physicists  have  calculated  the  number  of  waves  that  succeed  one  another 
for  each  of  the  several  prismatic  colors,  and  the  corresponding  wave- 
lengths ;  the  following  table  contains  the  results.  The  letters  A,  C,  D, 
etc.,  refer  to  Fraunhofer's  lines  (see  §  258). 

Length  of  waves  No.  of  waves 

in  millimeters.  per  second. 

Dark  red.  .  .  A 000760  .  .  .  395,000,000,000,000 

Orange  .  .  .  C 000656  .  .  .  458,000,000,000,000 

Yellow  .  .  .  D 000589  .  .  .  510,000,000,000,000 

Green  .  .  .  E 000527  .  .  .  570,000,000,000,000 

C.  Blue  .  .  .  F 000486  .  .  .  618,000,000,000,000 

U.  Blue  .  .  .  G 000431  .  .  .  697,000,000,000,000 

Violet.  .  .  .  H 000397  .  .  .  760,000,000,000,000 

There  is  a  limit  to  the  sensibility  of  the  eye  as  well  as  of 
the  ear. ,  The  range  of  vibrations  appreciable  by  the  eye  lies 
approximately  between  the  highest  and  the  lowest  numbers 
indicated  in  the  above  table  ;  i.e.  if  the  succession  of  waves 
be  much  more  or  much  less  rapid  than  is  indicated  by  these 
numbers,  the  sensation  of  sight  is  not  produced. 

It  is  evident  that  the  frequency  of  the  waves  emitted  by  a 
luminous  body,  and  consequently  the  color  of  the  light  emitted, 
must  depend  on  the  rapidity  of  the  vibratory  motions  of  the 
molecules  of  that  body,  i.e.  upon  its  temperature. 

This  has  been  shown  in  a  convincing  manner  as  follows  :  The  tem- 
perature of  a  platinum  wire  is  slowly  raised  by  passing  a  gradually 
increasing  current  of  electricity  through  it.  At  a  temperature  of  about 
540°  C..it  begins  to  emit  light;  and  if  the  light  be  analyzed  by  a  prism, 
it  is  shown  that  only  red  light  is  emitted.  As  the  temperature  rises, 
there  will  be  added  to  the  red  of  the  spectrum,  first  yellow,  then  green, 
blue,  and  violet,  successively.  When  it  reaches  a  white  heat,  it  emits  all 


SPECTRUMS.  243 

the  prismatic  colors.  It  is  significant  that  a  white-hot  body  emits  more 
red  light  than  a  red-hot  body,  and  likewise  more  light  of  every  color  than 
at  any  lower  temperature.  The  conclusion  is  that  a  body  which  emits 
white  light  sends  forth  simultaneously  waves  of  a  variety  of  lengths. 

253.  Continuous  Spectrums.     The   spectrum,   produced    by 
the  platinum  is  continuous ;   that  is,  the   band  of  light  is 
unbroken.     If  the  spectrum  be  not  complete,  as  when  the 
temperature  is  too  low,  it  will  begin  with  red,  and  be  con- 
tinuous as  far  as  it  goes.     All  luminous  solids  and  liquids  give 
continuous  spectrums. 

A  gas,  kerosene,  or  candle  flame  does  not  give  the  spectrum 
of  a  vapor,  but  gives  that  of  the  solid  particles  of  carbon  in  a 
state  of  incandescence ;  hence  the  continuous  spectrums  which 
these  flames  afford. 

254.  Spectroscopes.    Instruments  for  the  observation  of  spectrums 
are  called  spectroscopes.     The  essential  part  of  the  apparatus  is  the 
"dispersion  piece,"  which  is  usually  a  glass  prism.     Instead  of  looking 
at  the  spectrum  with  the  naked  eye,  it  is  usually  better  to  view  it  through 
a  small  telescope,  which  serves  to  magnify  it.     Fig.  203  represents  the 
simplest  form  of  the  Kirchhoff  and  Bunsen  spectroscope.     A  flint-glass 
prism,  A,  receives  light  through  an  adjustable  slit  at  the  end  of  a  tube,  B, 
called  the  collimator.     At  the  opposite  end  of  this  tube  is  a  converging 
lens,  and  the  slit  is  located  at  its  principal  focus,  so  that  rays  diverging 
from  the  slit  are  rendered  parallel  by  the  lens. 

It  is  often  necessary  to  have  some  means  of  determining  the  positions 
of  certain  lines  (to  be  described  hereafter)  observed  in  the  spectrum. 
The  usual  method  is  to  have  a  second  tube,  somewhat  like  the  collimating 
tube,  so  placed  that  the  rays  from  a  light  (e.g.  a  candle  flame,  C,  in  Fig. 
203),  after  passing  through  a  transparent  plate  (inside  the  tube),  on  which 
a  fine  scale  is  engraved,  and  through  a  lens,  by  which  they  are  made 
parallel,  are  reflected  from  the  nearest  face  of  the  prism,  and  pass  into 
the  telescope  along  with  the  beam  of  light  under  analysis.  Thus  the  eye 
while  viewing  the  spectrum  through  the  telescope  D  sees  also  a  magnified 
image  of  the  scale  coinciding  with  the  spectrum. 

255.  Bright-line  Spectrums.     If  a  platinum  wire  be  dipped 
in  a  solution  of  common  salt  and  placed  in  the  almost  color- 
less flame  of   a   Bunsen  burner   (Fig.  203),  the  flame  will 


244 


ETHER    DYNAMICS. 


become  colored  a  deep  yellow.  Examining  the  flame  with 
the  spectroscope,  you  find  instead  of  a  continuous  spectrum, 
such  as  is  described  in  §  253,  only  a  bright  narrow  line  of 
yellow  in  the  yellow  part  of  the  spectrum.  Your  spectrum 
consists  essentially  of  a  single  :  bright  yellow  line  on  a  com- 
paratively dark  ground.  (See  Sodium,  Plate  I,  frontispiece.) 


FIG.  203. 


Plate  I  also  exhibits  the  spectrums  obtained  when  salts  of  lithium, 
strontium,  and  potassium  are,  respectively,  introduced  into  the  flame. 
Each  of  these  salts  contains  a  different  metal ;  e.g.  common  salt  contains 
the  metal  sodium  ;  the  other  substances  used  successively  contain  respec- 

1  Spectroscopes  of  higher  dispersive  power  show  that  the  sodium  line  is  really  a 
double  line  divided  by  a  narrow  interval. 


SPECTRUM    ANALYSIS.  245 

lively  the  metals  lithium,  potassium,  and  strontium.  These  metals,  when 
introduced  into  the  flame,  are  vaporized,  and  we  get  their  spectrums 
when  in  a  gaseous  state.  All  incandescent  gases,  unless  under  great 
pressure,  give  discontinuous,  or  bright-line,  spectrums,  and  no  two  gases 
give  the  same  spectrum. 

256.  Spectrum  Analysis.    Molecules  of  different  substances, 
e.g.  sodium,  lithium,  etc.,  have  their  own  peculiar  rates  of 
vibration,  and  each  emits  ether-waves  whose  lengths  corre- 
spond to  the  rates  of  vibration,  and  hence  each  produces  its 
own  distinctive  bright-line  spectrum.      Hence  has  arisen  a 
new  chemical  analysis,  wherein  substances  are  detected   by 
observing  the  bright  lines  of  their  spectrums,  a  branch  of 
physical  chemistry  called  spectrum  analysis. 

It  is  only  in  the  gaseous  state,  however,  that  the  molecule  is  free  to 
exhibit  its  special  rate  of  vibration  ;  when  they  are  packed  closely 
together  in  a  solid  or  liquid,  their  motions  are  cramped,  their  periodicity 
is  lost,  and  all  manner  of  vibrations  are  induced.  Hence  spectrums  of 
solids  and  liquids  are  continuous,  i.e.  the  rates  of  vibrations  are  so  many 
in  number  as  to  leave  no  gaps  in  their  spectrums. 

Many  chemical  compounds  are  decomposed  into  their  elements,  and 
the  elements  are  rendered  gaseous,  at  a  temperature  that  is  at,  or  below, 
the  temperature  necessary  for  incandescence.  In  that  case  the  spectrum 
given  is  the  combined  spectrums  of  the  elements. 

257.  Reversed  or  Dark-line  Spectrum.    This  type  of  spectrum 
may  be  studied  as  follows  :  Arrange  apparatus  in  a  dark  room,  as  in  Fig. 
204.     N  is  the  nozzle  of  a  stereopticon  (p.  262)  containing  only  the  con- 
densing lens  ;  T  and  S  are  two  tin  plates,  in  the  latter  of  which  a  slit  is 
cut.     Allow  a  beam  of  calcium  light  to  pass  through  the  slit  in  S,  and 
thence  through  the  converging  lens  L  and  the  prism  P,  and  form  a  spec- 
trum on  a  screen,  H.     Hold  in  the  flame  of  a  Bunsen  burner,  B,  a  pellet 
of  sodium  ;  it  burns  vividly,  and  the  calcium  light  has  to  pass  through 
the  intensely  yellow  flame.     We  should  naturally  expect  that  the  yellow 
of  the  spectrum  would  now  be  more  intensely  illuminated,  but,  instead, 
a  dark  band  in  the  yellow  now  appears.     It  is  not  really  black,  but  com- 
paratively dark. 

Next  hold  the  plate  T  between  the  burner  and  the  condensers  so  that 
the  calcium  light  may  be  cut  off  from  the  upper  portion  of  the  slit,  leav- 
ing the  light  from  the  sodium  flame  alone  to  pass  through  this  part  of  the 


246 


ETHER    DYNAMICS. 


slit.  The  spectrum  R  formed  by  this  part  consists  of  a  bright  yellow 
line  on  a  dark  ground,  being  the  radiation  spectrum  of  sodium.  (It 
should  be  borne  in  mind  that  the  image  of  the  slit  is  inverted.)  The 
other  half,  A,  shows  a  dark  line  on  the  continuous  spectrum.  We  thus 
have,  contiguous  to  each  other,  the  bright-line  spectrum  of  sodium  and 
its  reversed,  dark-line, 'or  absorption  spectrum.  If  you  use  salts  of  lithium, 
potassium,  strontium,  etc.,  in  a  similar  manner,  in  every  case  you  will 
find  your  spectrum  crossed  by  dark  lines  where  you  would  expect  to  find 
bright  lines. 


FIG.  204. 


It  thus  appears  that  the  vapors  of  different  substances  absorb 
or  quench  the  very  same  rays  that  they  are  capable  of  emitting 
when  made  self-luminous,  very  much,  it  would  seem,  as  a 
given  tuning  fork  selects  from  various  sounds  only  those  of 
a  definite  wave-length  corresponding  to  its  own  vibration- 
period.  The  dark  places  of  the  spectrum  receive  light  in 
full  force  from  the  salted  flame  ;  but  the  light  is  so  feeble, 
in  comparison  with  those  places  illuminated  by  the  calcium 
light,  that  the  former  appear  dark  by  contrast.  Light  trans- 
mitted through  certain  liquids  (as  sulphate  of  quinine  and 
blood)  and  certain  solids  (as  some  colored  glasses)  produces 


FBAUNHOFER'S  LINES.  247 

band  spectrums.  These  spectrums  are  obtained  only  when 
light  passes  through  mediums  capable  of  absorbing  rays  of  a 
certain  wave-length ;  hence,  they  are  commonly  called  absorp- 
tion spectrums.  Since  a  given  vapor  causes  dark  lines  pre- 
cisely where  it  would  cause  bright  lines  if  ^it  were  itself  the 
only  radiator  of  light,  dark-line  spectrums  are  frequently 
called  reversed  spectrums.  There  are,  then,  three  kinds  of 
spectrums  :  continuous  spectrums,  produced  by  luminous  solids, 
liquids,  or,  as  has  been  found  in  a  few  instances,  gases  under 
great  pressure  ;  bright-line  spectrums,  produced  by  luminous 
vapors  ;  and  absorption  spectrums,  produced  by  light  that  has 
been  sifted  by  certain  mediums. 

258.  Fraunhofer's  Lines.  The  spectrum  of  sunlight,  when 
the  apparatus  employed  in  Experiment  1,  §  249,  is  properly 
adjusted,  is  observed  to  contain  a  large  number  of  dark 
lines  transverse  to  its  length.  These  were  first  mapped  by 
Fraunhofer  (1814),  who  distinguished  several  of  the  more 
prominent  ones  by  letters  of  the  alphabet ;  hence  the  dark 
lines  of  the  solar  spectrum  Have  received  the  name  of 
Fraunhofer 's  lines. 

So  far  as  has  been  discovered,  no  two  substances  have  a  spectrum  con- 
sisting of  the  same  combination  of  lines  ;  and,  in  general,  different  sub- 
stances very  rarely  possess  lines  appearing  to  be  common  to  both.  Hence, 
when  we  have  once  observed  and  mapped  the  spectrum  of  any  substance, 
we  may  ever  after  be  able  to  recognize  the  presence  of  that  substance 
when  emitting  light,  whether  it  is  in  our  laboratory  or  in  a  distant 
heavenly  body.1 

1  By  examination  of  the  reversed  spectrum  of  the  sun,  we  are  able  to  determine 
with  certainty  the  existence  there  of  sodium,  calcium,  copper,  zinc,  magnesium, 
hydrogen,  and  many  other  known  substances.  Again,  from  our  knowledge  of  the  way 
in  which  a  reversed  spectrum  can  be  produced,  we  may  conclude  that  the  sun  consists 
of  a  luminous  solid,  a  liquid,  or  an  intensely  heated  and  greatly  condensed  gas  (called 
a  photosphere),  fmd  that  this  nucleus  is  surrounded  by  an  atmosphere  of  cooler  vapor, 
in  which  exist  at  least  all  the  substances  just  named.  The  moon,  and  planets  that  are 
visible  only  by  reflected  sunlight,  give  the  same  spectrums  as  the  sun,  while  those 
that  are  self-luminous  give  spectrums  which  differ  from  the  solar  spectrum. 


248  ETHE&    DYNAMICS. 

259.  Infra-red  and  Ultra- violet  Rays.    The  energy  of  ether- 
waves   is  capable,  as   has  been  before  observed,  of  produc- 
ing calorific,  luminous,  or  chemical  effects,  according  to  the 
nature  of  the  bodies  upon  which  it  falls.     When  a  sensitive 
thermoscope  is  passed  along  the  spectrum,  heat  effects  are 
observed  throughout  the  visible  spectrum,  and  for  considerable 
distances   beyond   at  each  extremity.      All  ether-waves  are 
capable  of  producing  heating  effects. 

It  thus  appears  that  the  solar  spectrum  is  not  limited  to 
the  visible  spectrum,  but  extends  beyond  at  each  extremity, 
and  spectroscopic  analysis,  besides  sifting  the  waves  of  one 
color  from  those  of  another,  is  able  to  sift  out  rays  which 
do  not  produce  the  sensation  of  light  from  those  which  do. 
Those  rays  that  lie  beyond  the  red  are  called  the  infra-red 
rays,  while  those  that  lie  beyond  the  violet  are  called  the 
ultra-violet  rays.  The  infra-red  rays  are  of  longer  vibration- 
period,  and  the  ultra-violet  of  shorter  period,  than  the 
luminous  waves. 

260.  Only  One  Kind  of  Radiation.     The  fact  that  radiant 
energy  produces  three  distinct  effects  —  viz.  luminous,  heat- 
ing, and  chemical  —  has  given  rise  to  a  prevalent  idea  that 
there  are  three  distinct  kinds  of  radiation.     There  is,  how- 
ever, absolutely  no  proof  that  these  different  effects  are  pro- 
duced by  different  kinds  of  radiation.     Science  recognizes  in 
radiations  no  distinctions  but  periods,  wave-lengths,  and  wave- 
forms.     The  same  radiation  that  produces  vision  can  generate 
heat  and  chemical  action. 

The  fact  that  the  infra-red  and  ultra-violet  rays  do  not  affect  the  eye 
does  not  argue  that  they  are  of  a  different  nature  from  those  that  do,  but 
it  does  show  that  there  is  a  limit  to  the  susceptibility  of  the  eye  to 
receive  impressions  from  radiation.  Just  as  there  are  sound-waves  of 
too  long,  and  others  of  too  short  period  to  affect  the  ear,  so  there  are 
ether-waves,  some  of  too  long,  and  others  of  too  short  period  to  affect 
the  eye. 


COLOR  BY  ABSORPTION.  249 

SECTION  IX. 

COLOR. 

261.  Color  by  Absorption.  Color  is  a  sensation  ;  it  has  no 
material  existence.  The  term  "yellow  light"  means,  pri- 
marily, a  particular  sensation  ;  secondarily,  it  means  the 
physical  cause  of  this  sensation,  i.e.  a  train  of  ether-waves 
of  a  particular  frequency. 

Experiment  1.  By  means  of  a  porte-lumiere  introduce  a  beam  of 
sunlight  into  a  dark  room.  With  the  slit  and  prism  form  a  solar  spec- 
trum. Between  the  slit  and  the  prism  introduce  a  ruby-colored  glass ; 
all  the  colors  of  the  spectrum  except  the  red  are  much  reduced  in 
intensity. 

It  thus  appears  that  the  color  of  a  colored  transparent 
object,  as  seen  by  transmitted  light,  arises  from  the  unequal 
absorption  of  the  different  colors  of  white  light  incident  upon 
it.  A  red  glass  absorbs  less  red  light  than  light  of  other 
colors.  The  color  produced  by  absorption  is  rarely  very 
pure,  the  particular  hue  of  the  transmitted  light  being  due 
merely  to  a  predominance  of  certain  colors,  and  not  to  the 
absence  of  all  others.  As  the  absorbing  layer  is  thicker,  the 
resulting  color  is  purer  but  less  intense. 

Experiment  2.  We  have  found  that  common  salt  introduced  into  a 
Bunsen  flame  renders  it  luminous,  and  that  the  light  when  analyzed  with 
a  prism  is  found  to  contain  only  yellow.  Expose  papers  or  fabrics  of 
various  colors  to  this  light  in  a  darkened  room.  No  one  of  them  except 
yellow  exhibits  its  natural  color. 

Experiment  3.  Hold  a  narrow  strip  of  red  paper  or  ribbon l  in  the 
red  portion  of  the  solar  spectrum  ;  it  appears  red.  Slowly  move  it 
• toward  the  other  end  of  the  spectrum  ;  on  leaving  the  red  it  becomes 
darker,  and  when  it  reaches  the  green  it  is  quite  black  or  colorless,  and 
remains  so  as  it  passes  the  other  colors  of  the  spectrum.  Repeat  the 
experiment,  using  other  colors,  and  notice  that  only  in  light  of  its  own 
color  does  each  strip  of  paper  appear  of  its  natural  color,  while  in  all 
other  colors  it  is  dark. 

1  Care  must  be  exercised  to  select  only  pure  colors. 


250 


ETHER    DYNAMICS. 


FIG.  205. 


These  experiments  show  that  the  color  of  a  body  seen  by 
light  reflected  from  it  depends  both  upon  the  color  of  the 
light  incident  upon  it  and  upon  the  nature  of  the  body. 

If  a  piece  of  colored  glass,  A  B  (Fig.  205),  be  held  near  a 
window  so  as  to  receive  rays  of  sunlight  obliquely,  a  portion 

of  the  light  will  be 
reflected  by  the  ante- 
rior surface  of  the 
glass,  and,  falling  up- 
on the  white  ceiling, 
will  illuminate  it  with 
white  light.  Another 
portion  of  the  light 
will  enter  the  glass  and  be  reflected  from  the  posterior  sur- 
face ;  this  light,  having  entered  the  glass  and  traveled  in  it  a 
distance  a  little  greater  than  twice  its  thickness,  will  suffer 
an  unequal  absorption  of  its  rays,  and  after  emerging  from 
the  glass  will,  if  the  glass  be  blue,  illuminate  a  neighboring 
portion  of  the  ceiling  with  blue  light. 

This  illustrates  the  method  by  which  pigments  afford  3olor. 
Thus,  the  anterior  surface  of  a  water-color  drawing  rejects 
the  white  daylight.  Most  of  the  light  reflected  to  the  eye 
has,  however,  passed  through  the  pigment  to  the  white  paper 
beneath,  and,  being  reflected  from  this,  again  passes  through 
the  layer  of  pigment  before  reaching  the  eye.  Certain  of  the 
colors  which  compose  white  light  are  extinguished  while  pass- 
ing through  the  pigment,  and  the  color  by  which  the  pigment 
is  recognized  is  the  resultant  of  the  unextinguished  colors. 
This  is  technically  called  selective  absorption.  Different  pig- 
ments  quench  different  colors ;  the  unquenched  colors  deter- 
mine the  color  of  the  pigment. 

262.   Opalescence.    Sky  Colors. 

Experiment  4.  Dissolve  a  little  white  castile  soap  in  a  tumbler  of 
water ;  or,  better,  stir  into  the  water  a  few  drops  of  an  alcoholic  solution 
of  mastic,  enough  to  render  the  water  slightly  turbid.  Place  a  black 


OPALESCENCE.   SKY  COLORS.          251 

screen  behind  the  tumbler,  and  examine  the  liquid  by  reflected  sunlight, 
—  the  liquid  appears  to  be  blue  ;  examine  the  liquid  by  transmitted  sun- 
shine,—  it  now  appears  yellowish  red. 

Experiment  5.  Pour  some  of  the  turbid  liquid  into  a  small  test-tube, 
and  examine  it  and  the  tumbler  of  liquid  by  transmitted. light ;  the  former 
appears  almost  colorless,  while  the  latter  is  deeply  colored. 

When  a  medium  holds  in  suspension  fine  particles  of  mat- 
ter, the  shorter  light-waves  are  most  abundantly  reflected, 
giving  a  blue  color.  The  blue  is  purer  as  the  particles  are 
smaller.  Objects  seen  through  such  mediums  appear  of  the 
complementary  hue  (see  §  267).  This  phenomenon  is  called 
opalescence.  It  accounts  for  the  blue  of  watery  milk,  opa- 
lescent glass,  smoke,  and  the  sky. 

Skylight  is  reflected  light.  The  minute  particles  (of  water,  probably) 
that  pervade  the  atmosphere,  like  the  fine  particles  of  mastic  suspended 
in  the  water,  reflect  blue  light ;  while  beyond  the  atmosphere  is  a  black 
background  of  darkness.  But  we  must  not,  from  this,  conclude  that  the 
atmosphere  is  blue  ;  for,  unlike  blue  glass,  but  like  the  turbid  liquid,  it 
transmits  yellow  and  red  rays  freely,  so  that  seen  by  reflected  light  it  is 
blue,  but  seen  by  transmitted  light  it  is  yellowish  red. 

When  the  sun  is  near  the  horizon,  its  rays  travel  a  greater  distance  in 
the  air  to  reach  the  earth  than  when  it  is  in  the  zenith  (see  Fig.  189) ; 
consequently,  there  is  a  greater  loss  by  absorption  and  reflection  in  the 
former  case  than  in  the  latter.  But  the  yellow  and  red  rays  suffer  less 
destruction,  proportionally,  than  the  other  colors ; 
consequently,  these  colors  predominate  in  the  morning 
and  evening. 

263.  Mixing  Colors.  A  mixture  of  all  the 
prismatic  colors  in  the  proportion  found  in 
sunlight  produces  white.  Can  white  be  pro- 
duced in  any  other  way  ? 

Experiment  6.     On  a  black  surface,  A  (Fig.  206), 
lay  two  small  rectangular  pieces  of  paper,  one  yel- 
low and  the  other  blue,  about  2  inches  apart.     In  a 
vertical  position  between  these  papers,  and  from  3  inches  to  6  inches 
above  them,  hold  a  slip  of  plate  glass,  C.     Looking  obliquely  down 
through  the  glass  you  may  see  the  blue  paper  by  transmitted  light- 


252  ETHER    DYNAMICS. 

waves  and  the  yellow  paper  by  reflection.  That  is,  you  see  the  object 
itself  in  the  former  case,  and  the  image  of  the  object  in  the  latter  case. 
By  a  little  manipulation  the  image  and  the  object  may  be  made  to  over- 
lap each  other,  when  both  colors  will  apparently  disappear,  and  in  their 
place  the  color  which  is  the  result  of  the  mixture  will  appear.  In  this 
case  it  will  be  white,  or  rather  gray,  which  is  white  of  a  low  degree  of 
luminosity.  If  the  color  be  yellowish,  lower  the  glass  ;  if  bluish,  raise  it. 

Experiment  7.  With  the  rotating  apparatus,  rotate  the  disk  (Fig. 
207)  which  contains  only  yellow  and  blue.  The  colors  (i.e.  the  sensa- 
tions) so  blend  in  the  eye  as  to  produce  the  sensation  of  gray. 

Fig.  208  represents  "Newton's  disk,"  which  contains  the  seven  pris- 
matic colors  arranged  in  a  proper  proportion  to  produce  gray  when 
rotated. 


FIG.  207.  FIG.  208.  FIG.  209. 

In  like  manner,  you  may  produce  white  by  mixing  purple  and  green  ; 
or,  if  any  color  on  the  circumference  of  the  circle  (see  Complementary 
Colors,  Plate  I)  be  mixed  with  the  color  exactly  opposite,  the  resulting 
color  will  be  white.  Again,  the  three  colors,  red,  green,  and  violet, 
arranged  as  in  Fig.  209,  with  rather  less  surface  of  the  green  exposed 
than  of  the  other  colors,  will  give  gray.  Green  mixed  with  red,  in  vary- 
ing proportions,  will  produce  any  of  the  colors  in  a  straight  line  between 
these  two  colors  in  the  diagram  (Plate  I) ;  green  mixed  with  violet  will 
produce  any  of  the  colors  between  them ;  and  violet  mixed  with  red 
gives  purple. 

All  colors  are  represented  in  the  spectrum,  except  the  purple  hues. 
The  latter  form  the  connecting  link  between  the  two  ends  of  the  spec- 
trum. Our  color  chart  (Plate  I)  is  intended  to  represent  the  sum  total  of 
all  the  sensations  of  color.  By  means  of  this  chart  we  may  determine 
the  result  of  the  (optical)  mixture  of  any  two  colors,  as  follows  :  Find 
the  places  occupied  upon  the  chart  by  the  two  colors  which  are  to  be 
mixed,  and  unite  the  two  points  by  a  straight  line.  The  color  produced 
by  the  mixture  will  invariably  be  found  at  the  center  of  this  line. 


MIXING   PIGMENTS.  253 

264.  Mixing  Pigments. 

Experiment  8.  Mix  a  little  of  the  two  pigments  chrome  yellow  and 
ultramarine  blue,  and  you  obtain  a  green  pigment. 

The  last  three  experiments  show  that  mixing  certain  colors, 
and  mixing  pigments  of  the  same  name,  may  produce  very 
different  results.  In  the  first  experiments  you  mixed  colors  ; 
in  the  last  experiment  you  did  not  mix  colors,  and  we  must 
seek  an  explanation  of  the  result  obtained.  If  a  glass  vessel 
with  parallel  sides,  containing  a  blue  solution  of  sulphate  of 
copper,  be  interposed  in  the  path  of  the  light-waves  which 
form  a  solar  spectrum,  it  will  be  found  that  the  red,  orange, 
and  yellow  waves  are  cut  out  of  the  spectrum,  i.e.  the  liquid 
absorbs  these  waves.  And  if  a  yellow  solution  of  bichromate 
of  potash  or  picric  acid  be  interposed,  the  blue  and  violet 
waves  will  be  absorbed.  It  is  evident  that,  if  both  solutions 
be  interposed,  all  the  colors  will  be  destroyed  except  the 
green,  which  alone  will  be  transmitted  ;  thus  : 

Canceled  by  the  blue  solution,  l£  0  ^  G  B  V. 

Canceled  by  the  yellow  solution,       ,       R  O  Y  G  ^  X- 
Canceled  by  both  solutions,  $  0  V  G 


In  a  similar  manner,  when  white  light  strikes  a  mixture  of 
yellow  and  blue  pigments  on  the  palette,  it  penetrates  to  some 
depth  into  the  mixture  ;  and,  during  its  passage  in  and  out, 
all  the  colors  except  the  green  are  destroyed  ;  so  the  mixed 
pigments  necessarily  appear  green.  But  when  a  mixture  of 
yellow  and  blue  waves  enters  the  eye,  we  get,  as  the  result- 
ant of  the  combined  sensations  produced  by  the  two  colors, 
the  sensation  of  white  ;  hence,  a  mixture  of  yellow  and  blue 
gives  white. 

The  color  square  3  (Plate  I)  represents  the  result  of  the  mixture  of 
pigments  1  and  2  ;  while  4  represents  the  result  of  the  optical  mixture 
of  the  same  colors. 


254  ETHER   DYNAMICS. 

265.  Theory  of  Color- vision. 

The  generally  accepted  theory  of  color-vision  is  that  of  Dr.  Young 
(1801-2),  verified  by  Maxwell  and  Helmholtz.  It  supposes  the  exist- 
ence of  three  color  sensations,  red,  green,  and  violet.  These  excited 
simultaneously,  and  with  proper  intensities,  produce  the  sensation  of 
white  light.  Combined  in  twos,  they  produce  the  intermediate  color  sen- 
sations. Thus,  red  and  green  sensations  combined  give  yellow  or  orange  ; 
green  and  violet  give  blue,  etc.  The  longer  light-waves  excite  the  sensa- 
tion of  red  ;  together  with  those  somewhat  shorter,  they  excite  both  red 
and  green,  thus  giving  yellow,  and  so  on.  Strictly  speaking,  light-waves 
of  any  length  excite  all  three  sensations  ;  but  usually  either  one  or  two 
of  them  greatly  predominate. 

266.  Color  Blindness,     In  this  defect  in  vision,  one  of  the 
three  color  sensations  is  either  wanting  or  deficient,  usually 
that  of  red  ;  so  that  the  colors  perceived  are  reduced  to  those 
furnished  by  the  remaining  two  sensations,'  viz.  green  and 
violet.     This  causes  the  red-blind  person  to  confound  reds, 
greens,  and  grays.     In  some  rare  cases  the  sensation  of  green 
or  violet  is  the  one  deficient. 

267.  Complementary  Colors. 

Experiment  9.  On  a  piece  of  gray  paper  lay  a  circular  piece  of  blue 
paper  15  mm.  in  diameter.  Attach  one  end  of  a  piece  of  thread  to  the 
colored  paper,  and  hold  the  other  end  in  the  hand.  Place  the  eyes 
within  about  15  cm.  of  the  colored  paper,  and  look  steadily  at  the  center 
of  the  paper  for  about  fifteen  seconds  ;  then,  without  moving  the  eyes, 
suddenly  pull  the  colored  paper  away,  and  instantly  there  will  appear  on 
the  gray  paper  an  image  of  the  colored  paper,  but  the  image  will  appear 
to  be  yellow.  This  is  usually  called  an  after-image.  If  yellow  paper  be 
used,  the  color  of  the  after-image  will  be  blue  ;  and  if  any  other  color 
given  in  the  diagram  (Plate  I),  the  color  of  its  after-image  will  be  the 
color  that  stands  opposite  to  it. 

This  phenomenon  is  explained  as  follows :  When  we  look 
steadily  at  blue  for  a  time,  the  eyes  become  fatigued  by  this 
color,  and  less  susceptible  to  its  influence,  while  they  are  fully 
susceptible  to  the  influence  of  other  colors  ;  so  that  when  they 
are  suddenly  brought  to  look  at  white,  which  may  be  regarded 


CONTRASTING   COLORS.  255 

as  a  compound  of  yellow  and  blue,  they  receive  a  vivid  im- 
pression from  the  former,  and  a  feeble  impression  from  the 
latter ;  hence,  the  predominant  sensation  is  yellow.  Any  two 
colors  which  together  produce  white  are  said  to  be  comple- 
mentary to  each  other.  The  complement  of  green  is  purple 
—  a  compound  color  not  existing  in  the  spectrum.  The 
opposite  colors  in  the  diagram  (Plate  I)  are  complementary 
to  one  another. 

268.  Effect  of  Contrast.     When  different  colors  are  seen  at 
the  same  time,  their  appearance  differs  more  or  less  from  that 
observed  when  they  are  seen  separately.     Thus,  a  red  object 
(e.g.  a  red  rose)  appears  more  brilliant  if  a  green  object  be 
seen  in  juxtaposition  with  it.     Such  effects  are  said  to  be  due 
to  contrast. 

When  any  two  colors  given  in  the  circle  (Plate  I)  are 
brought  into  contrast,  as  when  they  are  placed  next  each 
other,  the  effect  is  to  move  them  farther  apart  in  the  color 
scale.  For  example,  if  red  and  orange  be  brought  in  con- 
trast, the  orange  assumes  more  of  a  yellowish  hue,  and  the 
red  more  of  a  purplish  hue.  Colors  that  are  already  as  far 
apart  as  possible,  e.g.  yellow  and  blue,  do  not  change  their 
hue,  but  merely  cause  each  other  to  appear  more  brilliant. 

269.  Colors  Produced  by  Interference.     We  recall  that  two 
sets  of  sound-waves  may  so  combine  as  to  neutralize  each 
other  and  produce  silence.     For  example,  the  phenomenon  of 
"  beats,'7  or  the  alternate  increase  or  diminution  of  intensity 
of  sound,  is  due  to  the  interference  of  two  sets  of  sound-waves 
in  the  same  and  opposite  phases  respectively.     If  radiation 
be   wave-motion,   similar   phenomena  ought  to  occur   under 
proper  conditions. 

Experiment  10.  Press  firmly  together  with  an  iron  clamp  two  pol- 
ished pieces  of  thick  plate  glass.  Bands  of  colors  will  be  seen  arranged 
around  the  point  of  pressure  in  curves  more  or  less  regular. 


256  ETHEft    DYNAMICS. 

Newton's  method  of  studying  these  colors  was  very  simple 
and  effective,  and  the  phenomena  exhibited  are  known  as 
"Newton's  rings."  By  this  method  a  convex  lens  of  very 
small  curvature  is  gently  pressed  upon  a  piece  of  plate  glass 
(Fig.  210),  and  beautiful  circular  interference  color  bands 


FIG.  210.  FIG.  211. 

encircle  the  point  of  contact  (Fig.  211).  It  will  be  seen  that 
the  film  of  air  between  the  lens  and  the  plate  increases  in 
thickness  from  the  point  of  contact  radially.  Now  if  light- 
waves be  incident  on  the  lens,  a  portion  will  be  reflected  from 
its  curved  surface  and  another  portion  from  the  surface  of  the 
plate -glass  on  which  the  lens  rests.  Since  the  latter  portion 
has  farther  to  travel  than  the  former  by  twice  the  thickness 
of  the  air-film  between  the  two  surfaces,  and  since  the  film 
gradually  increases  in  thickness  from  the  point  of  contact 
outward,  it  is  apparent  that  the  two  sets  of  reflected  waves 
will  meet  at  certain  places  in  like  phase  and  at  other  places 
in  opposite  phase,  causing  intensification  of  illumination  in 
the  former  instance  and  an  extinction  of  light  in  the  latter. 
If  the  incident  light  be  red,  a  series  of  concentric  red  rings 
will  alternate  with  dark  rings,  each  shading  off  into  the  other. 
If  violet  light  be  used,  the  color  rings  will  be  closer  together, 
since  the  wave-lengths  are  shorter.  If  white  light  be  used,  at 
every  point  some  one  color  will  be  destroyed,  leaving  its  com- 
plementary at  that  point.  Thus,  the  point  of  contact  between 
the  lens  and  plate  is  surrounded  by  rainbow-like  color  bands. 

Examples  of  color  produced  by  interference  :  Colors  of  the  soap- 
bubble,  of  a  film  of  oil  on  water,  of  oxides  formed  on  certain  metals 
when  heated,  and  of  striated  surfaces  like  mother-of-pearl. 


SOME   OPTICAL   INSTRUMENTS.  257 

SECTION   X. 
SOME    OPTICAL   INSTRUMENTS. 

270.  Compound  Microscope.  When  it  is  desired  to  magnify 
an  object  more  than  can  be  done 
conveniently  and  with  distinctness 
by  a  single  lens,  two  convex  lenses 
are  used,  —  one,  0  (Fig.  212),  called 
the  objective,  to  form  a  magnified 
real  image,  a'  b',  of  the  object  a  b  ; 
and  the  other,  E,  called  the  eye- 
piece, to  magnify  this  image  so  that 
the  image  a'  b'  appears  of  the  size 
a"  b".  Instead  of  looking  at  the 
object  as  when  we  use  a  simple 
lens,  we  look  at  the  real  inverted  image  (a'  b')  of  the  object. 

This  represents  the  simplest  possible  form  of  the  compound  micro- 
scope. In  practice,  however,  the  construction  is  more  complicated. 

Fig.  213  represents  a  perspective  and  a  sectional  view  of  a  simple  form 
of  a  modern  compound  microscope.  The  body  of  the  instrument  consists 
of  a  series  of  brass  tubes  movable  one  within  another.  In  the  upper  end 
H  is  the  ocular  or  eye-piece.  It  consists  of  two  plano-convex  lenses,  c 
and  n,  the  former  called  the  eye-lens,  the  latter  called  the  field-lens.1 

Microscopes  should  have  an  achromatic  objective.  This  consists  of 
two  to  four  achromatic  lenses  (the  achromatic  triplet,  the  most  common 
form,  is  represented  on  an  enlarged  scale  at  L  in  Fig.  213),  combined  so 
as  to  act  as  a  single  lens  of  short  focus.  By  the  use  of  several  lenses  the 
aberrations  can  be  better  corrected  than  with  a  single  lens. 

1  The  advantages  derived  from  the  use  of  two  lenses  in  the  eye-piece  are  as 
follows  : 

1.  The  combination  diminishes  spherical  aberration  and  thereby  increases  the 
flatness  of  the  field.      The  images  a'  b'  and  a"  b"  (Fig.  213)  are  in  reality  curved,  in 
consequence  of  the  spherical  aberration  caused  by  the  objective.    The  effect  of  the 
tield-lens  is  to  correct  this  curvature  in  a  measure. 

2.  The  combination  increases  the  field  of  view,  so  that  a  larger  area  of  the  object 
is  made  visible  at  the  same  view. 

3.  The  combination  diminishes  chromatic  aberration. 


258 


ETHER    DYNAMICS. 


The  object  to  be  examined  is  placed  on  a  stage,  S,  and,  if 
the  object  be  transparent,  it  is  strongly  illuminated  by  focus- 
ing light  upon  it  by  means  of  a  concave  mirror,  M.  If  the 
object  be  opaque,  it  is  illuminated  by  light  directed  upon  it 
obliquely  from  above  by  the  converging  lens  N. 


FIG.  213. 

271,  Magnifying  Power.  The  magnifying  power  of  a  com- 
pound microscope  is  the  product  of  the  respective  magnifying 
powers  of  the  object-glass  and  the  eye-piece  ;  that  is,  if  the 
first  magnify  20  times  and  the  other  10  times,  the  total 
magnifying  power  is  200.  The  magnifying  power  is  deter- 


TELESCOPES.  259 

mined  experimentally  by  means  of  a  micrometer  scale,  for 
a  description  of  which  the  student  is  referred  to  technical 
works  on  microscopy. 

272.  Telescopes.  Telescopes  are  used  to  view  (scope) 
objects  afar  off  (tele).  They  are  classified  as  astronomical 
or  terrestrial,  according  as  they  are  designed  to  be  used  in 
viewing  heavenly  bodies  or  terrestrial  objects  ;  reflecting  or 
ref r  acting ,  according  as  the  objective  is  a  concave  mirror  or 
a  converging  lens.  The  terrestrial  telescope  differs  from  the 
astronomical  in  producing  images  in  their  true  position  with- 
out inversion.  This  is  effected  by  means  of  an  extra  object 
lens,  which  corrects  the  inversion  of  the  main  object  lens. 
The  matter  of  inversion  is  of  little  or  no  consequence  in 
viewing  heavenly  bodies. 

The  refracting  astronomical  telescope,  like  the  compound 
microscope,  consists  essentially  of  two  lenses.  The  object- 
glass  O  (Fig.  214)  forms  a  real  diminished  image,  a  b,  of  the 


FIG.  214. 

object  A  B ;  this  image,  seen  through  the  eye-glass  E,  appears 
magnified  and  of  the  size  c  d.  The  object-glass  is  of  large 
diameter,  in  order  to  collect  as  much  light  as  possible  from  a 
distant  object  for  a  better  illumination  of  the  image. 

This  telescope  is  analogous  to  the  microscope,  but  the  two  instruments 
differ  in  this  respect  :  in  the  microscope,  the  object  being  very  near  the 
object-glass,  the  image  is  formed  much  beyond  the  principal  focus,  and 
is  greatly  magnified,  so  that  both  the  object-glass  and  the  eye-piece 
magnify  ;  while  in  the  telescope,  the  heavenly  body  being  at  a  great  dis- 
tance, the  incident  rays  are  practically  parallel,  and  the  image  formed 


260 


ETHER    DYNAMICS. 


by  the  object-glass  is  much  smaller  than  the  object.  The  only  magnifi- 
cation which  can  occur  is  produced  by  the  eye-piece,  which  ought  there- 
fore to  be  of  high  power.  The  magnify  nig  power  of  this  instrument 
equals  approximately  the  focal  length  of  the  object-glass  divided  by  the  focal 
length  of  the  eye-piece. 

273.  The  Human  Eye.  Fig.  215  represents  a  horizontal 
section  of  this  wonderful  organ.  Covering  the  front  of  the 
eye,  like  a  watch-crystal,  is  a  transparent  coat,  I,  called  the 
cornea.  A  tough  membrane,  2,  of  which  the  cornea  is  a  con- 
tinuation, forms  the  outer  wall 
of  the  eye,  and  is  called  the 
sclerotic  coat,  or  "white  of  the 
eye."  This  coat  is  lined  on  the 
interior  with  a  delicate  mem- 
brane, 3,  called  the  choroid  coat  ; 
the  latter  consists  of  a  black 
pigment,  which  prevents  inter- 
nal reflection.  The  inmost  coat 
4,  called  the  retina,  is  formed 
by  expansion  of  the  optic  nerve 
O.  The  muscular  tissue  i  i  is 
called  the  iris ;  its  color  determines  the  so-called  "color  of 
the  eye."  In  the  center  of  the  iris  is  a  circular  opening,  5, 
called  the  pupil,  whose  function  is  to  regulate,  by  involun- 
tary enlargement  and  contraction,  the  quantity  of  light-waves 
admitted  to  the  posterior  chamber  of  the  eye.  Just  back  of 
the  iris  is  a  tough,  elastic,  and  transparent  body,  6,  called 
the  crystalline  lens.  This  lens  divides  the  eye  into  two  cham- 
bers ;  the  anterior  chamber  7 -is  filled  with  a  limpid  liquid 
called  the  aqueous  humor ;  the  posterior  chamber  8  is  filled 
with  a  jelly-like  substance  called  the  vitreous  humor.  The 
lens  and  the  two  humors  constitute  the  refracting  apparatus. 
The  eye  may  be  likened  to  a  photographer's  camera,  in 
which  the  retina  takes  the  place  of  the  sensitized  plate. 
Images  of  outside  objects  are  projected  by  means  of  the 


FIG. 215. 


DEFECTS    OF    VISION.  261 

crystalline  lens,  assisted  by  the  refraction  of  the  humors, 
upon  this  screen,  and  the  impressions  thereby  made  on  this 
delicate  membrane  of  nerve  filaments  are  conveyed  by  the 
optic  nerve  to  the  brain.  Fig.  216  illustrates  the  manner 


OBJECT 


FIG.  216. 

in  which  the  image  of  an  object  is  formed  on  the  retina, 
except  that  no  attempt  is  made  to  represent  the  several 
refractions.  It  will  be  seen  that  the  image  is  inverted,  but 
by  some  mental  act  it  is  made  to  appear  upright. 

With  the  ordinary  camera  the  distance  of  the  lens  from 
the  screen  must  be  regulated  to  adapt  itself  to  the  varying 
distances  of  outside  objects,  in  order  that  the  images  may  be 
properly  focused  on  the  screen.  In  the  eye  this  is  accom- 
plished by  changing  the  convexity  of  the  lens.  We  can 
almost  instantly  and  unconsciously  change  the  lens  of  the 
eye  so  as  to  form  on  the  retina  a  distinct  image  of  an  object 
miles  away,  or  of  one  only  a  few  inches  distant.  The  nearest 
limit  at  which  an  object  can  be  placed  so  as  to  form  a  dis- 
tinct image  on  the  retina  is  about  five  inches.  On  the  other 
hand,  the  normal  eye  in  the  passive  state  is  adjusted  for 
objects  at  an  infinite  distance. 

274.  Defects  of  Vision.  Myopia  (short-sightedness)  is  caused  by 
the  excessive  length  of  the  globe  from  front  to  back,  so  that  the  images 
of  all  but  near  objects  are  formed  in  front  of  the  retina.  Remedy  :  use 
diverging  lenses.  Hypermetropia  (long-sightedness)  occurs  when  the  axis 
of  the  globe  is  so  short  that  the  image  of  an  object  is  back  of  the  retina 
unless  the  object  is  held  at  an  inconvenient  distance,  in  which  case  it 


262 


ETHER    DYNAMICS. 


tends  to  become  indistinct.    Remedy  :  use  converging  lenses.    Presbyopia 
is  due  to  loss  of  accommodation  power,  so  that  while  vision  for  distant 

objects  remains  clear,  that  for  near  objects 
is  indistinct.  This  defect  is  incident  to 
advancing  years,  and  is  due  to  progressive 
loss  of  elasticity  of  the  crystalline  lens. 
Remedy  :  converging  lenses.  Astigmatism 
is  caused  by  an  inequality  in  the  curvature 
of  the  cornea  in  different  meridians,  so 
that  when,  for  example,  a  diagram  like 
Fig.  217  is  held  at  a  distance,  vertical  lines 
will  be  in  focus  and  horizontal  lines  will 
be  out  of  focus  and  will  appear  blurred 
and  indistinct,  or  vice  versa.  Remedy  : 
lenses  of  cylindrical  curvature.  But,  for  this,  as  well  as  for  all  other 
defects  or  troubles  of  the  eyes,  consult  a  skilled  oculist,  and  the  earlier 
the  better. 

Advice  to  all :  Do  not  overstrain  or  overtax  the  eyes,  or  use  them  in 
insufficient  or  excessive  light,  in  nickering  light  such  as  that  of  a  gas-jet, 
or  in  unsteady  light  such  as  that  in  a  moving  vehicle  ;  and  avoid,  so  far 
as  practicable,  sudden  changes  of  light,  such  as  lightning  flashes,  etc. 

275.  Stereopticon.  This  instrument  is  extensively  employed 
in  the  -lecture  room  for  producing  on  a  screen  magnified 
images  of  small,  transparent  pictures  on  glass,  called  slides  ; 


FIG.  217. 


FIG.  218. 


also  for  rendering  a  certain  class  of  experiments  visible  to 
a  large  audience  by  projecting  them  on  a  screen.  The  lime 
light  is  most  commonly  used,  though  the  electric  light  is 


HEAT   NOT   TRANSMITTED   BY   RADIATION.          263 

preferred  for  a  certain  class  of  projections.  The  flame  of  an 
oxyhydrogen  blowpipe,  A  (Fig.  218),  is  directed  against  a 
stick  of  lime,  B,  and  raises  it  to  a  white  heat.  The  radiations 
from  the  lime  are  condensed  by  means  of  a  convex  lens,  C, 
called  the  condensing  l&ns  (usually  two  plano-convex  lenses 
are  used),  so  that  a  larger  quantity  of  radiations  may  pass 
through  the  convex  lens  E,  called  the  projecting  lens.  The 
latter  lens  produces  (or  projects)  a  real,  inverted,  and  mag- 
nified image  of  the  picture  on  the  screen  S.  The  mounted 
lens  E  may  slide  back  and  forth  on  the  bar  F  so  as  properly 
to  focus  the  image. 

SECTION  XI. 

THERMAL   EFFECTS   OF   RADIATION. 

276.  Heat  not  Transmitted  by  Radiation.    We  have  learned 
that  heat  may  travel  through  matter   (by  conduction)   and 
with  matter  (by  convection),  and  it  is  sometimes  stated  that 
there  is  a  third  method  by  which  it  travels,  viz.  "  radiation." 
Heat  itself  is  not  transferred  by  radiation  at  all ;  heat  gen- 
erates radiation  (i.e.  ether-waves)  at  one  place,  and  radiation 
produces  heat  at  another  ;  it  is  radiation  which  travels,  not 
'heat.     It  does  not  exist  as  heat  in  the  intervening  space,  and 
therefore  does  not  necessarily  heat  the  substance  filling  that 
space.     Heat  can  flow  only  one  way,  viz.  from  a  given  point 
to  a  point  that  is  colder ;  radiation  travels  in  all  directions. 
The  sun  sends  us  no  heat,  but  it  sends  radiations  which  the 
earth  transforms  into  heat  ;  but  it  should  be  borne  in  mind 
that  while  they  are  radiations  they  are  not  heat,  and  vice  versa. 

277.  Diathermancy  and  Athermancy.    The  character  of  any 
given  body  determines  largely  what  becomes  of  the  radia- 
tions which  strike  it.     If  the  nature  of  the  body  be  such 
that  its  molecules  can  accept  the  motion  of  the  ether,  the 
ether  vibrations   are   said  to   be  absorbed  by  the  body,  and 


264  ETHER    DYNAMICS. 

the  body  is  thereby  heated ;  i.e.  the  undulations  of  ether  are 
transformed  into  molecular  energy,  or  heat.  Glass,  for  instance, 
allows  the  sun's  radiations  to  pass  very  freely  through  it,  and 
very  little  is  transformed  into  heat.  But  if  the  glass  be  cov- 
ered with  the  soot  of  a  candle  flame,  the  soot  will  absorb  the 
radiations,  and  the  glass  become  heated.  Observe  IIOAV  cold 
window-glass  may  remain,  while  radiations  pour  through  it 
and  heat  objects  in  the  room.  Only  those  radiations  that  a 
body  absorbs  heat  it ;  those  that  pass  through  it  do  not  affect  its 
temperature.  Bodies  that  transmit  radiations  freely  are  said 
to  be  diathermanous ,  while  those  that  absorb  them  largely  are 
called  athermanous. 

These  terms  bear  the  same  relation  to  the  transmission  of  radiant 
energy  of  any  and  all  wave-lengths  as  do  transparency  and  opacity  to 
the  transmission  of  light  or  visible  radiations.  The  most  diathermanous 
substance  known  is  rock  salt.  A  solution  of  iodine  in  carbon  bisulphide 
absorbs  almost  completely  the  rays  of  the  visible  spectrum,  but  transmits 
almost  completely  the  invisible  infra-red  rays.  A  plate  of  alum  acts  in 
the  reverse  manner,  transmitting  the  visible  and  absorbing  the  invisible. 
Among  liquids  carbon  bisulphide  is  exceptionally  transparent  to  all  forms 
of  radiation  ;  while  water,  transparent  to  short  waves,  absorbs  the  longer 
waves,  and  is  thus  quite  athermanous. 

Experiment  1.  Bring  the  bulb  of  an  air  thermometer  into  the  focus 
of  a  burning-glass  exposed  to  the  sun's  rays.  The  radiation  concentrated 
on  the  enclosed  air  scarcely  affects  this  delicate  instrument. 

Experiment  2.  Cover  the  outside  of  the  bulb  of  the  air  thermom- 
eter with  lampblack  and  repeat  the  last  experiment.  The  lampblack 
absorbs  the  radiant  energy,  and  the  heat  conducted  through  the  glass  to 
the  enclosed  air  raises  its  temperature  and  causes  it  to  expand  and  rapidly 
push  the  liquid  out  of  the  stem. 

Dry  air  is  almost  perfectly  diathermanous.  All  of  the 
sun's  radiations  that  reach  the  earth  pass  through  the  atmos- 
phere, which  contains  a  vast  amount  of  aqueous  vapor.  This 
vapor,  like  water,  is  comparatively  opaque  to  long  waves  ; 
hence  it  modifies  very  much  the  character  of  the  radiations 
which  reach  the  earth. 


I    UNIVERSITY  ffl 


ALL    BODIES    EMIT    RADIATIONS.          '  265 

This  fact,  together  with  what  we  have  learned  from  Experiment  1, 
enables  us  to  understand  the  method  by  which  our  atmosphere  becomes 
heated.  First,  that  portion  of  the  radiant  energy  from  the  sun  which 
comes  to  us  in  the  form  of  relatively  long  waves  is  stopped  by  the  watery 
vapor  in  the  air,  which  is  thereby  heated.  The  portion  that  comes  to  us 
in  short  waves,  escaping  this  absorption,  heats  the  earth  in  falling  upon  it. 
The  warmed  earth  loses  its  heat  —  partly  by  conduction  to  the  air,  still 
more  largely  by  radiation  outward.  The  form  of  radiation,  however, 
has  been  greatly  changed  ;  for  now,  coming  from  a  body  at  a  low  tem- 
perature, it  is  chiefly  in  long  waves  that  the  energy  is  transmitted  ;  while, 
as  we  have  seen,  it  was  largely  in  the  form  of  short  waves  that  the  earth 
received  its  heat.  But  it  is  exactly  these  long  waves  which  are  most 
readily  absorbed  by  the  atmosphere  ;  hence  the  atmosphere,  or  rather  the 
aqueous  vapor  of  the  atmosphere,  acts  as  a  sort  of  trap  for  the  energy 
which  conies  to  us  from  the  sun. 

Remove  the  watery  vapor  (which  serves  as  a  "blanket"  to  the  earth) 
from  our  atmosphere,  and  the  chill  resulting  from  the  rapid  escape  of 
heat  by  radiation  would  probably  put  an  end  to  all  animal  and  vegetable 
life.  Glass  does  not  screen  us  from  the  sun's  heat,  but  it  can  very 
effectually  screen  us  from  the  heat  radiated  from  a  stove  or  any  other 
terrestrial  object.  Glass  is  diathermanous  to  the  sun's  radiations  (simply 
because  they  have  already  lost  most  of  the  very  long  waves  by  atmos- 
pheric absorption),  but  quite  athermanous  to  other  radiations.  This  is 
well  illustrated  in  the  case  of  hotbeds  and  greenhouses.  The  sun's 
rays  pass  through  the  glass  of  these  enclosures  almost  unobstructed,  and 
heat  the  earth  ;  but  the  radiations  given  out  in  turn  by  the  earth  are  such 
as  cannot  pass  out  through  the  glass,  and  hence  the  heat  is  retained 
within  the  enclosures. 

278.  All  Bodies  Emit  Radiations,  Hot  bodies  usually  part 
with  their  heat  much  more  rapidly  by  radiation  than  by  all 
other  processes  combined.  But  cold  bodies,  like  ice,  emit 
radiations,  even  when  surrounded  by  warm  bodies.  This 
must  be  so  from  the  nature  of  the  case,  for  all  bodies  that 
we  are  acquainted  with  are  at  some  temperature ;  their  mole- 
cules are  therefore  in  a  state  of  motion,  and  being  sur- 
rounded by  ether  they  cannot  move  without  imparting  some 
of  their  motion  to  the  ether.  But  in  order  that  a  body 
become  colder  by  radiation  it  must  lose  more  heat  by  radia- 
tion than  it  receives, 


266  ETHEK    DYNAMICS. 

279.  Prevost's  Theory  of  Exchanges,     Let  us  suppose  that 
we  have  two  bodies,  A  and  B,  at  different  temperatures  —  A 
warmer  than  B.     Radiation  takes  place,  not  only  from  A  to  B, 
but  from  B  to  A ;  but,  in  consequence  of  A's  excess  of  tem- 
perature, more  radiation  passes  from  A  to  B  than  from  B  to 
A,  and  this   continues  until  both  bodies  acquire  the  same 
temperature.     At  this  point  radiation  by  no  means  ceases, 
but  each  now  gives  as  much  as  it  receives,  and  thus  equilib- 
rium is  kept  up.     This  is  known  as  "  Prevost's  Theory  of 
Exchanges." 

280.  Good  Absorbers ;  Good  Radiators. 

Experiment  3.  Select  two  small  tin  boxes  of  equal  capacity, —  one 
should  be  bright  outside,  while  the  other  should  be  covered  thinly  with 
soot  from  a  candle  flame.  Cut  a  hole  in  the  cover  of  each  box  large 
enough  to  admit  the  bulb  of  a  thermometer.  Fill  both  boxes  with  hot 
water,  and  introduce  into  each  a  thermometer.  They  will  register  the 
same  temperature  at  first.  Set  both  in  a  cool  place,  and  in  half  an  hour 
you  will  find  that  the  thermometer  in  the  blackened  box  registers  several 
degrees  lower  than  the  other.  Then  fill  both  with  cold  water,  and  set 
them  in  front  of  a  fire  or  in  the  sunshine,  and  it  will  be  found  that  the 
temperature  in  the  blackened  box  rises  the  more  rapidly. 

As  bodies  differ  widely  in  their  absorbing  power,  so  they 
do  in  their  radiating  power,  and  it  is  found  to  be  universally 
true  that  good  absorbers  are  good  radiators,  and  bad  absorbers 
are  bad  radiators.  In  both  cases  much  depends  upon  the 
character  of  the  surface  as  well  as  of  the  substance.  Bright, 
polished  surfaces  are  poor  absorbers  and  poor  radiators  ; 
while  tarnished,  dark,  and  roughened  surfaces  absorb  and 
radiate* rapidly.  Dark  clothing  absorbs  and  radiates  more 
rapidly  than  light  clothing. 

EXERCISES. 

1.  What  objections  can  you  raise  to  the  term  "radiant  heat"? 

2.  Explain  why  the  temperature  of  a  hotbed  is  above  that  of  the  sur- 
rounding air. 

3.  How  could  you  separate  the  dark  radiation  of  an  electric  arc  lamp 
from  the  luminous  radiation  ? 


GENERAL    EXERCISES.  267 

4.  How  can  you  demonstrate  the  existence  of  ether-waves  of  greater 
length  than  the  light-giving  waves  ? 

5.  Ice  appears  to  radiate  cold.    Explain  the  phenomenon  by  Pre'vost's 
theory. 

6.  What  parts  of  the  spectrum  are  invisible  to  the  eye  ? 

7.  How  can  you  prove  the  existence  of  invisible  solar  rays  ? 

GENERAL   EXERCISES. 

1.  What  is  light  ? 

2.  State  points  of  resemblance  and  points  of  difference  between  light- 
waves and  sound-waves.      Which  can  traverse  a  vacuum  (as  regards 
matter)  ? 

3.  Two  books  are  held,  respectively,  2  feet  and  7  feet  from  the  same 
gas  flame.     Compare  the  intensities  of  the  illumination  of  their  respec- 
tive pages. 

4.  (a)  What  is  the  general  effect  of  a  concave  mirror  on  light- waves  ? 
(b)  What  kind  of  lens  produces  a  similar  effect  ? 

5.  How  can  a  beam  of  light  be  bent  ? 

6.  When  red  and  green  sensations  coexist,  what  is  the  resulting  sen- 
sation ? 

7.  Why  do  white  surfaces  appear  gray  at  twilight  ? 

8.  How  are  objects  heated  by  the  sun  ? 

9.  What  evidences  can  you  give  that  the  earth  receives  energy  from 
the  sun  ? 

10.  What  phenomenon  shows  that  ether- waves  do  not  traverse  all 
substances  with  equal  speed  ? 

11.  Why  does  not  winking  interfere  with  vision  ? 

12.  What  effect  has  the  refractive  action  of  the  atmosphere  upon  the 
apparent  position  of  the  sun  arid  the  duration  of  daylight  ? 

13.  A  small  bright  image  of  the  sun  is  projected  on  a  card  held  16 
inches  from  a  convex  lens.     How  far  must  the  card  be  held  from  the 
lens  to  receive  a  distinct  image  of  a  candle  flame  which  is  at  a  distance 
of  18  inches  from  the  lens  ? 

14.  Account  for  the  dazzling  whiteness  of  snow. 

15.  What  is  the  focal  distance  of  a  convex  lens  when  the  distances  of 
the  image  and  object  are,  respectively,  5  and  36  cm.  from  the  lens  ? 

16.  A  candle  flame   illuminates   a  screen   15  inches  distant.     How 
many  candle  flames  at  a  distance  of  5  feet  would  be  required  to  produce 
an  equal  illumination  ? 

17.  (a)  What  do  we  mean  by  a  white  body  ?     (b)  What  by  a  black 
body  ?     (c)  What  is  meant  by  white  light  ? 


CHAPTER  VII. 
ELECTROSTATICS. 


SECTION   I. 

INTKODUCTION. 

281.  Electrification.    Certain  bodies,  provided  the  conditions 
are  suitable,  acquire  by  contact  and  subsequent  separation  (or 
more  readily  by  friction)  the  property  of  attracting  light  bodies, 
such  as  pieces  of  tissue  paper,,  etc.    For  example,  glass  rubbed 
with  silk,  and  sealing  wax  or  ebonite  rubbed  with  woolen 
cloth,  manifest  this  property  by  picking  up  scraps  of  paper, 
etc.     Bodies  in  this  state  are  said  to  be  electrified,  or  charged 
with  electricity.    An  electric  charge  is  supposed  to  be  due  to  a 
strained  condition  of  the  ether  surrounding  the  charged  body.1 

Experiment  1.  Rub  a  rubber  comb  with  a  woolen  cloth,  or  draw  it 
a  few  times  through  your  hair  (if  dry).  Hold  the  comb  over  a  handful 
of  bits  of  tissue  paper  ;  the  papers  quickly  jump  to  the  comb,  stick  to  it 
for  an  instant,  and  then  leap  energetically  from  it.  The  papers  are  first 
attracted  to  the  comb,  but  in  a  short  time  acquire  some  of  its  electrifica- 
tion, and  then  are  repelled. 

282.  Two  Kinds  of  Electrification. 

Experiment  2.  Suspend  a  ball  of  elder  pith,  C  (Fig.  219),  by  a 
silk  thread.  Electrify  a  glass  rod,  D,  with  a  silk  handkerchief,  and  pre- 
sent it  to  the  ball  ;  attraction  at  first  occurs,  followed  by  repulsion  soon 
after  contact.  Next  excite  a  stick  of  sealing  wax  or  a  rubber  comb  with 
a  woolen  cloth  and  present  it  to  the  ball,  which  is  repelled  by  the  elec- 
trified glass ;  the  ball  is  attracted  by  the  electrified  wax  or  rubber.2 

1  The  electric  charge  has  its  origin  in  the  contact  of  dissimilar  molecules. 

2  "  When  two  substances  have  different  molecular  velocities  at  their  common 
surface  of  mutual  contact,  the  molecules  hamper  one  another,  and  energy  is  lost ; 
this  energy  takes  the  form  of  energy  of  electrical  displacement."  — 


ELECTRIFICATION  A  FORM  OF  POTENTIAL  ENERGY.     269 


FIG.  219. 


It  is  evident  (1)  that  there  are  two  kinds  of  electrification; 
(2)  that  bodies  similarly  electrified  repel  one  another,  and  that 
bodies  oppositely  electrified  attract  one  another. 

Glass  rubbed  with  silk  is  said  to  receive  a  vitreous  charge.  On 
the  other  hand,  the  wax,  on  being  rubbed  with  woolen  cloth, 
receives  a  resinous  charge. 
The  vitreous  charges  are 
said  to  be  positive  (-+-  E), 
and  the  resinous  charges 
negative  (—  E). 

Experiment  3.  Once  more 
electrify  a  stick  of  sealing  wax 
with  a  woolen  cloth,  and  pre- 
sent it  to  the  pith  ball,  and 
after  the  ball  is  repelled  bring 
the  surface  of  the  flannel 
which  had  electrified  the  rod 

near  the  ball ;  the  ball  is  attracted  by  it,  showing  that  the  rubber  is  also 
electrified,  and  with  the  opposite  kind  to  that  which  the  sealing  wax 
possesses. 

One  hind  of  electrification  is  never  developed  alone.  When 
two  substances  are  rubbed  together,  and  one  becomes  electri- 
fied, electrification  of  the  opposite  kind  is  always  developed 
on  the  other. 

283.  Electrification  a  Form  of  Potential  Energy.  When 
small  pieces  of  glass  and  silk  are  rubbed  together,  it  is  found 
that  after  they  are  pulled  apart  they  attract  each  other  with 
a  definite  and  measurable  force,  and  that  this  force  varies 
inversely  as  the  square  of  the  distance  between  them. 

The  strained  ether  between  them  is  thought  to  operate  like 
strained  India-rubber  bands,  pulling  the  two  bodies  together. 
Work  is  required  in  order  to  separate  the  excited  bodies,  and 
the  bodies  thus  separated  possess  potential  energy  of  electrical 
separation. 


2TO 


ETHER    DYNAMICS. 


284.  What  is  Electricity  ?  The  student  naturally  asks  this 
never-answered  question.1  Provisionally  we  shall  regard  elec- 
tricity as  that  which  is  transferred  from  one  body  to  another 
body  when  the  two  become  oppositely  electrified.  Electricity 
is  not  a  form  of  energy.2  It  is  quite  true  that  electricity 
under  pressure  or  in  motion  possesses  energy  ;  in  the  same 

sense  water  and  air  under  like 
conditions  possess  energy,  but 
no  one  presumes  to  call  them 
forms  of  energy. 

Our  methods  of  "produc- 
ing electricity  "  are,  so  far  as 
we  know,  merely  methods  of 
disturbing  electrical  equilib- 
rium. 

285.  The  Electroscope.  This 
is  an  instrument  used  to  de- 
tect the  presence  of  electrifi- 
cation in  a  body,  and  to  deter- 
mine its  kind.  It  usually 

consists  of  two  strips  of  gold  foil,  A  B  (Fig.  220),  suspended 
from  a  brass  rod  within  a  glass  jar.  To  the  upper  end  of  the 
rod  is  fixed  a  metal  disk,  C.  On  the  opposite  sides  of  the 
interior  of  the  jar  are  two  strips  of  metal  foil,  D  and  E,  of 
sufficient  hight  to  be  touched  by  the  strips  A  and  B  on  their 
extreme  divergence. 

(1)  If  an  unelectrified  body  be  brought  near  the  disk  C,  no 
change  takes  place  in  the  two  strips  of  foil  A  and  B ;  but  if  an 
electrified  body  be  brought  near  the  disk,  the  strips  diverge, 

1 "  This  is  at  once  an  important  and  a  difficult  question.  Many  who  ask  it  never 
doubt  the  existence  of  electricity.  To  the  scientific  mind  the  question  presents  itself 
rather  in  the  form  —  Is  there  such  a  thing  as  electricity  ?  Cannot  electrical  phe- 
nomena be  traced  back,  like  all  others,  to  the  properties  of  the  ether  and  of  ponder- 
able matter  ?  "  —HERTZ. 

2  There  is  no  mechanical  equivalent  of  a  quantity  of  electricity,  as  there,  is  of  a 
quantity  of  heat ;  but  there  is  a  mechanical  equivalent  of  electrical  energy. 


T 


FIG.  220. 


CONDUCTION.  271 

thus  indicating  the  existence  of  a  charge  of  electricity  in 
the  body. 

(2)  If  the  electroscope  be  charged  by  contact  with  an 
excited  body,  the  strips  will  remain  in  a  divergent  posi- 
tion. While  they  are  in  this  condition,  if  a  body  similarly 
charged  be  brought  near  the  disk,  the  strips  will  diverge 
more;  but  if  an  unexcited  body  or  a  body  oppositely  elec- 
trified be  brought  near  the  disk,  the  strips  will  collapse. 

286.  Conduction, 

Experiment  4.  (a)  Rub  a  brass  tube,  held  in  the  hand,  with  warm 
silk.  Bring  it  near  the  disk  of  the  electroscope  ;  the  leaves  are 
unaffected.  (6)  Wrap  a  piece  of  sheet  rubber  around  one  end  of  the 
tube  and  hold  this  end  in  the  hand,  and  rub  as  before.  Bring  it  near  the 
disk  of  the  electroscope  ;  notice  that  the  leaves  diverge,  (c)  Repeat 
the  last  operation,  but  before  bringing  the  tube  near  the  disk  touch  the 
tube  with  a  finger  ;  the  leaves  no  longer  show  signs  of  electrification. 

In  the  first  (a)  and  last  (c)  operations  electricity  escaped 
through  the  hand  and  body  to  the  earth  ;  in  the  second  (b)  it 
was  prevented  from  escaping  by  the  intervening  sheet  rubber. 
Substances  which  allow  electricity  to  spread  over  them,  i.e.  sub- 
stances which  offer  little  resistance  to  the  flow  of  electricity, 
are  called  conductors.  Those  which  offer  great  resistance  to 
its  passage  are  called  non-conductors,  insulators,  or  dielectrics. 

Some  of  the  best  insulating  substances  are  dry  air,  ebonite, 
shellac,  resins,  paraffine,  glass,  silks,  and  furs.  On  the  other 
hand,  metals  are  exceedingly  good  conductors.  Moisture 
injures  the  insulation  of  bodies  ;  hence,  experiments  suc- 
ceed best  on  dry,  cold  days  of  winter,  when  the  moisture  of 
the  air  is  least  liable  to  be  condensed  on  the  surfaces  of 
apparatus,  especially  if  the  latter  be  kept  warm. 

Water  cannot  be  retained  in  a  reservoir  unless  its  walls 
be  of  sufficient  strength  ;  so  a  body,  in  order  to  retain  a 
charge  of  electricity,  must  be  surrounded  by  something  that 
will  offer  sufficient  resistance  to  the  escape  of  electricity. 


272 


ETHEk    DYNAMICS. 


This  entity  which  corresponds  to  the  walls  of  the  reser- 
voir is  termed  the  dielectric.  It  may  be  the  air  or  any  of 
the  so-called  non-conductors  of  electricity.  A  body  thus 
surrounded  is  said  to  be  insulated.  There  is  no  limit  to  the 
quantity  of  electricity  with  which  a  body  can  be  charged, 
provided  the  charge  be  not  conducted  away. 

SECTION   II. 
INDUCTION. 

287.  Electricity  Acts  across  a  Dielectric. 

Experiment  1.  Figure  221  represents  an  empty  eggshell  covered 
with  tin  foil  to  make  it  a  good  conductor.  It 
is  suspended  from  a  glass  rod  by  a  silk  thread. 
(a)  Electrify  a  glass  rod  and  bring  it  near  the  shell. 
The  shell  moves  toward  the  rod.  (b)  Next  intro- 
duce a  glass  plate  between  the  rod  and  shell.  The 
shell  approaches  the  rod  as  before. 

_  The  chief  lesson  we  learn  from  this  ex- 

periment  is    that   electricity   acts   across  a 
dielectric.     In  (a)  the  dielectric  was  air  ;  in  (b),  air  and  glass. 

288.  To  Determine  what  actually  Happens  on  an  Insulated 
Conductor  when  an  Electrified  Body  is  Brought  Near. 

Experiment  2.  (a)  Suspend,  as  above,  two  shells  so  as  to  touch 
each  other,  end  to  end,  as  in  Fig.  222, 
thus  making  practically  one  conductor. 
Bring  near  to  one  end  of  the  shells  a 
sealing-wax  rod,  D,  excited  with  —  E. 
While  the  rod  is  in  this  position  carry 
a  thin  strip  of  tissue  paper,  C,  along 
the  shells.  The  paper  is  attracted  to 
the  shells,  but  most  strongly  at  the 
ends.  In  the  middle  of  the  conductor, 
where  the  shells  touch  each  other,  there  is  little  if  any  electrification. 

(b)  While  the  rod  D  is  still  in  position,  separate  B  from  A,  then 
remove  D.  Test  each  shell  with  the  tissue  paper  ;  both  are  found  to  be 
excited. 


FIG.  222. 


CHARGING   BY   INDUCTION.  273 

(c)  Charge  an  electroscope   with  +  E.      Then  bring  A  near  it ;    the 
leaves  diverge,  showing  that  A  is  charged  with  +  E.     Bring  B  near  the 
electroscope  ;  the  leaves  collapse,  showing  that  B  is  charged  with  —  E. 

(d)  Finally  bring  the  two  shells  near  each  other;  they  attract  each 
other.     Allow  them  to  touch  each  other,  and  then  test  each  with  the 
tissue  paper  or  the  electroscope  ;  it  will  be  found  that  both  have  become 
discharged. 

From  the  above  operations  we  learn  that  when  an  electri- 
fied body  is  brought  near  but  not  in  contact  with  an  insulated 
conductor,  the  electrified  body  acts  across  the  dielectric  upon 
the  conductor,  repelling  electricity  of  the  same  kind  to  the 
remote  side  of  the  conductor,  and  attracting  the  opposite  kind 
to  the  side  near  to  it.  Such  electrical  action  is  called  induc- 
tion. The  electrified  body  which  produces  the  action  is  called 
the  inducing  body  ;  the  charge  of  electricity  thus  produced 
is  called  induced  electricity. 

289.  Charging  by  Induction. 

Experiment  3.  Take  a  proof  plane,  E  (Fig.  223)  (which  consists  of 
an  insulating  handle  of  glass  or  gutta-percha,  terminating  at  one  end 
with  a  thin  metal  disk,  F,  about  the  size 
of  a  5-cent  nickel),  and  connect  it  with 
an  electroscope,  G,  by  a  fine  wire,  H. 
Bring  a  stick  of  sealing  wax  electrified 
as  before  with  —  E  near  the  eggshell 
conductor.  Holding  the  proof  plane  by 
the  insulating  handle,  bring  the  disk  near  FlG  223 

the  end  of  the  conductor  charged  by  in- 
duction with  —  E.  The  —  E  will  act  inductively  upon  the  continuous 
conductor  consisting  of  disk,  wire,  and  electroscope,  charging  the  end 
nearest  itself  (i.e.  the  disk)  with  +E  and  the  remote  end  (i.e.  the  leaves) 
with  —  E.  The  leaves  of  the  electroscope  show  the  presence  of  a  charge 
by  their  divergence. 

Now,  while  everything  is  in  the  position  indicated  by  the  cut,  touch 
with  the  finger  any  part  of  the  continuous  conductor  ;  the  leaves  of  the 
electroscope  instantly  collapse.  The  —  E  with  which  the  leaves  had  been 
charged,  being /ree,  is  discharged  through  your  body.  But  the  +  E  con- 
centrated on  the  disk  of  the  proof  plane  is  bound  by  the  attraction  of  the 


274  ETHER   DYNAMICS. 

charge  of  —  E  on  the  end  of  the  shell  nearest  it,  and  cannot  escape. 
Remove  the  finger  from  the  electroscope  and  the  proof  plane  from  the 
influence  of  the  shell ;  the  leaves  again  diverge. 

The  last  phenomenon  is  explained  as  follows  :  After  —  E 
has  been  discharged  from  the  continuous  conductor,  there  is 
left  an  excess  of  +  E ;  but  this  excess  is  all  concentrated  in 
the  disk  F  so  long  as  it  remains  near  the  negative  charge 
of  the  shell.  But  as  soon  as  F  is  removed  from  the  influ- 
ence of  the  shell,  the  charge  spreads  over  the  entire  con- 
ductor, and  the  leaves,  which  receive  a  portion  of  the 
charge,  diverge.  The  conductor  is  said  to  be  charged  by 
induction. 

Experiment  4.  To  electrify  the  shell  by  induction,  bring  the  excited 
wax  near  it,  touch  the  shell  with  a  finger,  remove  the  ringer,  and  finally 
remove  the  rod.  The  proof  plane  being  connected  with  the  electroscope 
and  being  charged  with  —  E,  bring  F  near  to  the  shell  A  ;  the  leaves  col- 
lapse, showing  that  the  shell  is  charged  with  +  E,  which  draws  the  —  E 
away  from  the  leaves. 

Observe  that  when  a  body  becomes  charged  by  induc- 
tion the  charge  which  it  receives  is  opposite  in  kind  to  that 
of  the  inducing  body. 

290.  Charging  by  Conduction. 

Experiment  5.  Disconnect  the  proof  plane  from  the  electroscope. 
Charge  the  electroscope  with  —  E  and  the  shell  with  +  E ;  touch  the 
shell  with  the  disk  of  the  proof  plane,  then  hold  the  disk 
near  the  electroscope ;  the  divergent  leaves  collapse, 
showing  that  the  disk  bears  +  E  which  it  received  by 
conduction  from  the  shell  when  they  were  brought  in 
contact.  Of  course  the  charge  is  the  same  kind  as  that 
of  the  body  which  communicated  it. 

291.  Induction  Precedes  Attraction.    When  a 
PIG.  224.         pjth  ball  is  brought  near  an  electrified  glass 
rod,  the  +  E  on  the  rod  A  (Fig.  224)  induces  —  E  on  the  side 
of  the  ball  B,  nearest  A,  and  repels  +  E  to  the  farther  side. 


ELECTRICAL   POTENTIAL.  275 

The  +  E  of  A  and  the  —  E  of  B  therefore  attract  each  other  ; 
likewise  the  -j-  E  of  A  and  the  +  E  of  B  repel  each  other ;  but 
since  the  former  charges  are  nearer  each  other  than  the  latter 
are,  the  attraction  exceeds  the  repulsion. 


SECTION   III. 

ELECTRICAL   POTENTIAL. 

292.  Electrostatics  and  Electro-kinetics.    Electricity  may 
be  at  rest,  as  in  a  charged  body,  or  it  may  be  in  motion,  as  in 
the  case  of  a  charged  body  connected  by  a  conductor  with  the 
earth,  when  it  is  discharged  through  the  conductor  to  the 
earth.     It  will  be  shown  later  on  that  as  long  as  a  flow  of 
electricity  continues,  the  conductor  along  which  it  flows  has 
prpperties  different  from  those  of  a  simple  electrified  body. 
That  branch  of  electrical  science  which  treats  of  the  proper- 
ties of  simple  electrified  bodies  is  called  Electrostatics,  because 
in  these  bodies  electricity  is  supposed  to  be  at  rest ;  and  that 
branch  which  treats  of  electricity  in  motion  is  called  Electro- 
kinetics. 

293.  Potential.    The  fundamental  fact  of  electricity  is  that 
we  are  able  to  place  bodies  in  different  electrical  conditions.     A 
charge  of  electricity  (which  implies   an  abnormal  electrical 
condition)  is  the  foundation  of  all  electrical  phenomena.     We 
are  now  to  discuss  the  meaning  and  use  of  the  very  important 
term  potential,  as  it  is  employed  in  electrical  science. 

a.  When  a  charged  conductor  is  connected  with  the  earth, 
a  transfer  of  electricity  takes  place  between  the  body  and 
the  earth. 

b.  If  the  body  be  charged  with  +  E,  we  say  arbitrarily 
that  electricity  passes  from  the 'body  to  the  earth  ;  but  if  the 
body  be  charged  with  —  E,  we  say  that   electricity  passes 
from  the  earth  to  the  body. 


276  ETHER    DYNAMICS. 

c.  If  two  insulated  charged  conductors  be  connected  with 
each  other,  electricity  may  or  may  not  pass  from  one  to  the 
other.     Whether  electricity  passes  from  one  to  the  other, 
and  in  what  direction  it  passes,  if  at  all,  depends  upon  the 
so-called  potentials  of  the  conductors. 

d.  If  two  bodies  have  the  same  potential,  no  transfer  of 
electricity  takes  place  between  them  ;  but  if  they  have  dif- 
ferent potentials,  there  will  be  a  transfer,  and  the  body  from 
which  the  electricity  flows  is  said  to  be  at  a  higher  potential 
than  the  body  to  which  it  flows. 

294.  Definition  of  Potential.    The  potential  of  a  conductor 
may,  therefore,  be  denned  provisionally  as  the  electrical  con- 
dition of  that  conductor  which  determines  the  direction  of  the 
transfer  of  electricity. 

The  term  potential  is  relative.  It  is  important  to  have 
a  standard  of  reference  whose  potential  is  considered  to  be 
zero,  just  as  it  is  convenient  in  stating  the  elevations  or 
depressions  of  the  earth's  surface  to  give  the  distances  above 
or  below  sea  level,  which  is  taken  as  the  zero  of  hight.  For 
experimental  purposes  the  earth  is  usually  assumed  to  be  at 
zero  potential.  A  body  charged  with  -f  E  is  understood  to 
be  one  that  has  a  higher  potential  than  that  of  the  earth,  and 
a  body  charged  with  —  E  is  one  that  has  a  lower  potential 
than  that  of  the  earth.  * 
.  .*  * 

295.  Analogies.     Potential  is  analogous,  in  many  respects, 
to  (1)  temperature  and  to  (2)  liquid  level. 

(1)  When  we  say  that  the  temperature  of  air  is  20°  or 
-  10°  C.,  we  mean  that  its  temperature  is  20°  above  or  10° 
below  the  standard  temperature  of  reference,  viz.  that  of 
melting  ice.  If  two  bodies  at  different  temperatures  be 
placed  in  thermal  communication,  heat  will  pass  from  the 
body  at  a  higher  temperature  to  the  one  at  a  lower,  and  will 
continue  to  do  so  until  both  are  at  the  same  temperature. 


LIGHTNING.  277 

(2)  If  two  vessels  containing  water  at  different  levels 
be  put  in  communication  at  their  bottoms  by  a  pipe,  water 
will  flow  from  the  one  at  a  higher  level  to  the  one  at  a 
lower  until  the  water  is  at  the  same  level  in  both  vessels. 

Temperature  is  not  heat ;  level  is  not  water  ;  and  potential 
is  not  electricity,  but  merely  the  state  of  the  conductor  which 
determines  the  direction  of  transfer  of  electricity.  (See 
definition  of  temperature,  §  126.) 

SECTION   IV. 
ATMOSPHERICAL   ELECTRICITY. 

296,  Lightning.  Franklin,  by  his  historic  experiment  with 
the  kite,  in  1752,  proved  the  exact  similarity  of  lightning 
and  thunder  to  the  light  and  crackling  of  the  electric  spark. 
Certain  clouds  which  have  formed  very  rapidly  are  highly 
charged,  usually  with  -f-  E,  but  sometimes  with  —  E.  The 
surface  of  the  earth  and  objects  thereon  immediately  beneath 
the  cloud  are,  of  course,  charged  inductively  with  the  opposite 
kind  of  electricity.  The  opposite  charges  on  the  earth  and 
on  the  cloud  hold  each  other  prisoners  by  their  mutual 
attraction,  the  air  serving  as  an  intervening  dielectric. 

As  condensation  progresses  in  the  cloud  its  potential  rises 
(or  sinks).  This  process  continues  till  the  difference  of 
potential  between  the  cloud  and  the  earth  becomes  great 
enough  to  produce  a  discharge  through  the  air. 

It  is  the  accumulation  of  induced  charges  on  elevated 
objects,  such  as  buildings,  trees,  etc.,  that  offers  an  intensi- 
fied attraction  for  the  opposite  electricity  of  the  cloud  in 
consequence  of  their  greater  proximity,  and  renders  such 
objects  especially  liable  to  be  struck  by  lightning. 

The  clouds  gather  electricity  from  the  atmosphere.  Our 
knowledge  of  the  method  by  which  the  atmosphere  becomes 
charged  is  very  limited, 


278  ETHER   DYNAMICS. 

We  see  what  we  call  a  "flash. of  lightning."  What  we 
really  see  is  merely  particles  of  air  heated  temporarily  to 
incandescence.  Lightning  strokes  last  for  a  very  brief  time, 
—  perhaps  a  millionth  of  a  second,  —  though  the  sensation 
produced  on  the  retina  of  the  eye  lasts  longer. 

Lightning  rods  may  be  very  effective  in  protecting  build- 
ings from  lightning  strokes,  since  electricity  is  more  likely  to 
pass  along  the  rods  of  metal,  which  are  good  conductors,  than 
through  the  building.  But  the  rods  should  either  run  sev- 
eral feet  into  water  or  be  connected  with  a  large  metal  plate 
buried  deep  in  a  stratum  of  earth  that  is  always  moist. 
Lightning  rods  may  be  worse  than  useless  unless  there  is 
a  good  electrical  connection  between  them  and  the  earth. 

EXERCISES. 

1.  Our  knowledge  of  the  existence  of  electricity,  and  the  possibility 
of  employing  electric  energy  in  the  performance  of  nearly  every  species  of 
work,  are  due  to  what  fundamental  fact  ? 

2.  (a)  Is  the  energy  of  a  charge  of  electricity  potential  or  kinetic  ? 
(6)  In  what  is  a  charge  of   electricity  supposed  to  consist  ?     (c)  How 
does  the  energy  of  a  charge  differ  from  the  energy  of  a  discharge  ? 

3.  State  in  full  the  difference  in  the  operations  of  charging  by  con- 
duction and  charging  by  induction. 

4.  When  a  discharge  takes  place,   what  becomes  of  the  electric 
energy  ? 

5.  State  how  it  may  be  shown  that  there  are  two  kinds  of  electrifi- 
cation. 

6.  To  what  is  electrical  potential  analogous  ? 

7.  How  can  you  ascertain  the  kind  of  electrification  a  body  has  ? 

8.  Do  electrostatics  and  electro-dynamics  treat  of  different  kinds  or 
different  states  of  electricity  ? 

9.  On  what  condition  will  electricity  pass  from  one  body  to  another 
body;    or  from  a  point  in  a  given  body  to  another  point  in  the  same 
body? 

10.  (a)  When  glass  is  electrified  by  rubbing  it  with  silk,  does  its 
potential  become  higher  or  lower  than  that  of  the  earth  ?  (b)  Has  seal- 
ing wax,  after  being  rubbed  with  woolen  cloth,  a  higher  or  a  lower  poten- 
tial than  that  of  the  earth  ? 


BENJAMIN    FRANKLIN. 


CHAPTER  VIII. 

ENERGY  OP  ELECTRIC  FLOW.     ELECTRO- 
KINETICS. 


SECTION  I. 
VOLTAIC.  CELLS.      ELECTRIC   CIRCUITS. 

297.  Introductory  Experiments. 

APPARATUS  REQUIRED.  A  tumbler  f  full  of  water,  into  which  have 
been  poured  two  or  three  tablespoonf  uls  of  strong  sulphuric  acid ;  a  strip 
of  sheet-copper,  and  two  pieces  of  rolled  zinc,  each  about  5  inches  long, 
1|  inches  wide,  and  at  least  T\  of  an  inch  thick  (a  piece  of  No.  16  copper 
wire  12  inches  long  should  be  sol- 
dered to  one  end  of  each  piece  of 
metal,  and  the  soldering  covered 
with  asphaltum  paint)  ;  2  yards  of 
silk-insulated  No.  18  copper  wire  ; 

two  double  connectors  (Fig.  225),  which  serve  to  join  two  wires  without 
the  inconvenience  of  twisting  them  together.  One  of  the  zincs  should 
be  amalgamated  as  follows :  First  dip  the  zinc,  with  the  exception  of 
\  inch  at  the  soldered  end,  into  the  acidulated  water ;  then  pour  mer- 
cury over  the  wet  surface,  and  finally  rub  the  surface,  now  wet  with 
mercury,  with  a  cloth.  (To  ensure  complete  amalgamation,  it  is  best  to 
repeat  this  operation.) 

Experiment  1.  (a)  Put  the  unamalgamated  zinc  into  the  tumbler 
containing  acidulated  water.  Bubbles  of  hydrogen  gas  arise  from  the 
surface  of  the  zinc. 

(6)  Remove  this  zinc  and  introduce  the  amalgamated  zinc.  No  bub- 
bles (or  at  least  very  few)  arise  from  the  latter  (provided  that  the  zinc  be 
properly  amalgamated). 

(c)  Put  the  copper  strip  into  the  liquid,  but  do  not  allow  the  two 
metals  or  their  wires  to  touch.  No  bubbles  arise  from  either  metal. 
Connect  the  wires  of  the  two  metals  with  a  double  connector  ;  copious 


280  ETHER    DYNAMICS. 

bubbles  arise  from  the  copper  strip,  but  very  few  from  the  zinc  strip. 
Bubbles  escaping  from  the  copper  seem  to  indicate  that  chemical  action 
is  taking  place  between  the  metal  and  the  liquid.  But  experience  will 
teach  you  that  the  appearance  is  deceptive,  as  you  will  find  that  in  no 
case  is  copper  consumed. 

(d)  Substitute  the  unamalgamated  zinc  for  the  amalgamated  ;  bub- 
bles rise  abundantly  from  the  surfaces  of  both  the  zinc  and  copper. 

Lesson  Learned.  Unamalgamated  zinc  is  acted  on  by  the 
liquid  under  all  circumstances  ;  amalgamated  zinc  is  not 
acted  on  by  the  liquid  unless  the  copper  strip  is  also  in  the 
liquid,  and  not  then  unless  the  metals  be  connected.  If  then 
we  would  at  any  time  stop  the  action,  we  have  only  to  dis- 
connect the  metals.  It  seems  also  that  the  wire  connecting 
the  two  metals  serves  some  important  purpose  in  keeping  up 
this  action. 

If  plates  of  two  dissimilar  metals  be  placed  in  a  liquid  of  a 
class  which  we  will  term  an  electrolyte  (I.e.  one  which  is  capa- 
ble of  being  decomposed  by  a  current  of  electricity),  it  may 
be  shown  by  actual  experiment *  that  the  free  end  of  the  wire 
connected  with  one  plate  is  charged  with  +  E,  and  the  free 
end  of  the  wire  connected  with  the  other  plate  is  charged 
with  —  E.  Hence,  in  the  experiment  above  we  conclude  that 
if  the  two  oppositely  charged  bodies  be  brought  into  contact, 
i.e.  if  the  free  end  of  the  wire  leading  from  the  copper  plate 
(called  the  positive  electrode]  be  brought  to  touch  the  free  end 
of  the  wire  leading  from  the  zinc  (called  the  negative  elec- 
trode), a  discharge  will  occur  between  the  oppositely  charged 
bodies.  In  this  case,  however,  the  discharge  is  a  continuous 
one  ;  in  other  words,  there  is  a  continuous  flow  or  current  of 
electricity  as  long  as  the  contact  is  preserved. 

That  difference  in  quality  in  virtue  of  which  zinc  and 
copper  placed  in  acidulated  water  can  give  rise  to  an  elec- 
tric current  is  called  their  electro-chemical  difference,  and 

1  See  author's  "  Principles  of  Physics,"  p.  463- 


THE    VOLTAIC    CELL.  281 

the  zinc  is   said  to  be  electro-positive  to  the   copper  in  the 
liquid.1 

298.  The  Voltaic  Cell.  Two  solids  differing  electro-chemi- 
cally  (of  which  zinc  is  almost  invariably  one)  placed  in  an 
electrolytic  liquid  constitute  what  is  called  a  galvanic  or 
voltaic*  cell  (or  pair).  One  of  these  plates  must  be  more 
actively  attacked  by  the  liquid  than  the  other;  the  plate 
most  acted  upon  is  called  the  electro-positive  element,  and  the 
other  the  electro-negative  element. 

The  greater  the  disparity  between  the  two  elements  with 
reference  to  the  action  of  the  liquid  on  them,  the  greater  the 

Terence  in  potential ;  hence  the  greater  the  current. 


In  the  following  electro-motive  series  the  substances  are  so  arranged 
that  the  most  electro-positive,  or  those  most  affected  by  dilute  sulphuric 
acid,  are  at  the  beginning,  while  those  most  electro-negative,  or  those 
least  affected  by  the  acid,  are  at  the  end.  The  arrow  indicates  the 
direction  of  the  current  through  the  liquid. 

B 

tH  3  fl 

<D            p            rH 
+    0  ~  .          'O  g<          0>          •£          ,0 


It  will  be  seen  that  zinc  and  carbon  are  the  two  substances  best 
adapted  to  give  a  strong  current. 

When  the  wires  from  the  two  plates  are  joined,  the  dis- 
charge of  the  two  plates  would  produce  electrical  equilib- 
rium were  there  not  some  means  of  maintaining  a  difference 

1  The  nomenclature  in  use,  by  which  the  zinc  plate  is  called  the 
electro-positive  element  and  at  the  same  time  the  negative  pole  of  the 
combination,  is  at  first  perplexing  to  the  student.    Let  him  bear  in 
mind  that  electricity  always  flows  from  a  point  of  high  potential  to  a 
point  of  relatively  low  potential.     For  example,  let  a  current  origi- 
nating in  a  voltaic  cell  at  point  a  (Fig.  226)  follow  the  direction  indi- 
cated by  the  arrows  ;  then  point  c  must  be  negative  with  reference  to 
point  a,  but  positive  with  reference  to  point  d ;  again,  point  d,  while 
negative  to  point  c,  is  positive  to  point  e! 

2  A  single  voltaic  couple  is  usually  termed  a  cell;  a  combination  of 

cells,  a  battery.  FIG.  226. 


282  ETHEEf  DYNAMICS. 

of  potential  between  the  two  plates.  This  is  accomplished 
by  the  chemical  action  between  the  liquid  and  the  electro- 
positive element,  and  at  the  expense  of  the  chemical  poten- 
tial energy  of  the  electrolyte.  A  voltaic  cell  is,  therefore, 
a  contrivance  which  converts  potential  energy  of  chemical 
separation  into  electrical  energy. 

299.  Electrical  Circuit.  This  term  is  applied  to  the  entire 
path  along  which  electricity  flows,  and  it  comprises  the  bat- 
tery itself  and  the  wire  or  other  conductor  connecting  the 
elements.1  The  operations  of  bringing  the  two  extremities  of 
the  wire  into  contact  and  separating  them  are  called,  respec- 
tively, closing  and  opening,  or  making  and  breaking,  the  circuit. 
Opening  a  circuit  at  any  point  and  filling  the  gap  with  an 
instrument  of  any  kind,  so  that  the  current  is  obliged  to 

traverse  it,  is  called  introducing  the  instrument  into 

the  circuit. 

300.  Importance  of  Amalgamating  the  Zinc.  Com- 
mercial zinc  contains  impurities,  such  as  carbon,  iron,  etc. 
Fig.  227  represents  a  zinc  element  having  on  its  surface  a 
particle  of  carbon,  A,  purposely  magnified.  If  such  a  plate 
FIG  227  ke  immerse(l in  dilute  sulphuric  acid,  the  particles  of  carbon 
will  form  with  the  zinc  numerous  voltaic  circuits.  This 
occasions  a  great  waste  of  materials,  because,  when  the  regular  circuit 
is  broken,  local  action,  as  it  is  called,  still  continues.  If  mercury  be 
rubbed  over  the  surface  of  the  zinc,  it  dissolves  a  portion  of  the  zinc, 
forming  with  it  a  semi-liquid  amalgam,  which  covers  up  the  impurities. 

301.  Polarization  of  the  Negative  Element. 

Experiment  2.  Construct  a  voltaic  cell  composed  of  dilute  sulphuric 
acid  and  plates  of  copper  and  zinc.  Introduce  into  the  circuit  a  gal- 
vanoscope  (§  310)  and  note  the  deflection  of  the  needle  when  the  circuit 

JIt  was  an  early  discovery  in  telegraphic  history  that  a  complete  metallic  circuit 
is  not  necessary,  but  that,  in  common  parlance,  the  earth  can  be  used  as  a  "  return 
circuit."  This  type  of  circuit  is  represented  by  a  cell  with  a  wire  leading  from  one 
element  to  any  convenient  point  of  the  e'arth,  and  a  second  wire  leading  from  the 
other  element  to  any  other  point  of  the  earth,  even  though  it  be  many  miles  distant 
from  the  first  point. 


CELLS.  283 

is  first  closed.  Watch  the  needle  for  a  time.  Little  by  little  this  deflec- 
tion decreases,  and  meantime  bubbles  of  hydrogen  gas  collect  on  the 
copper  plate.  This  accumulation  of  gas  gives  rise  to  what  is  called 
"  polarization  of  the  negative  element  or  plate." 

We  already  understand  that  difference  of  potential  is  in- 
dispensable to  a  flow  of  electricity.  Difference  of  potential 
gives  rise  to  something  analogous  to  a  force,  which  causes  the 
flow  of  electricity.  The  greater  the  difference  of  potential, 
the  greater  is  this  agent  which  puts  the  electricity  in  motion. 
But  a  deposit  of  hydrogen  on  the  copper  raises,  in  some 
measure,  the  potential  of  this  (negative)  element  and  thereby 
diminishes  the  potential  difference  between  the  two  elements. 
Hence,  the  current  is  (in  technical  language)  "  weakened." 

The  remedy  for  this  is  to  prevent  the  deposit  of  hydrogen 
upon  the  negative  element.  The  usual  method  is  to  employ 
in  addition  to  the  dilute  sulphuric  acid  (i.e.  the  exciting 
liquid)  some  substance  which  will  combine  with  the  hydro- 
gen as  soon  as  it  is  liberated.  A  substance  used  for  this 
purpose  is  termed  a  depolarizer.  A  mixture  of  a  solution 
of  crystals  of  potassium  dichromate  in  water  with  a  suitable 
quantity  of  sulphuric  acid  is  used  as  a  depolarizer  in  the 
so-called  dichromate  cells. 

302.  Grenet  Cell,     This  is  a  potassium  dichromate  cell  in  which 
two  carbon  plates,  C  C  (Fig.  228),  electrically  con- 
nected, and  a  zinc  plate,  Z,  suspended  between  them 

by  a  brass  rod,  A,  are  immersed  in  the  mixed  liquid 
referred  to  above. 

This  combination  furnishes  a  much  more  energetic 
and  constant  current  than  would  be  furnished  if  only 
dilute  sulphuric  acid  were  used. 

303.  Bunsen  Cell.     A  plan  generally  adopted 
to  keep  the  depolarizing  liquid  away  from  the  zinc 
plate,  where  it  is  not  wanted  and  only  does  harm,  is  to 
place  the  carbon  plate  in  an  unglazed,  porous,  earthen 
cup,  and  to  surround  it  with  the  depolarizing  sub- 
stance.    This  arrangement,  called  a  two-fluid  cell,  is  that  adopted  by 
Bunsen  (Fig.  229)  and  others. 


284 


ETHEfc   DYNAMICS. 


304.  Leclanche  Cell.  There  is  a  class  of  galvanic  cells  in  which 
the  negative  element  is  protected  from  polarization  by  means  of  metallic 
oxides.  Of  these  the  best  known  is  the  Leclanche'  cell  (Fig.  230).  In 
this  cell  the  carbon  plate  C  is  contained  in  a  porous  cup,  P,  and  packed 


PIG.  229 


FIG.  230. 


round  with  fragments  of  gas-retort  coke  and  manganese  peroxide.  The 
manganese  compound  has  a  strong  affinity  for  the  hydrogen.  Neverthe- 
less, the  elements  quickly  polarize  when  in  action. 
They  need  periodical  rest  to  recover  their  normal 
condition.  Such  are  called  open-circuit  cells, 
since  they  are  suited  for  work  only  on  lines  kept 
open  or  disconnected  most  of  the  time,  as  in* 
telephone  and  bell-ringing  circuits.  The  zinc 
rod  Z  is  immersed  in  a  solution  of  ammonium 
chloride,  which  is  the  exciting  liquid. 

305.  Daniell  Cell. 

Leaving  the  hydrogen-generating  batteries, 
we  will  examine  briefly  another  form  incapable 
of  this  species  of  polarization.  The  Daniell  cell 
(Fig.  231)  uses  a  solution  which,  instead  of  depos- 
iting hydrogen,  deposits  copper  upon  a  copper 
negative  plate,  and  hence  is  free  from  hydrogen  polarization.  It  contains 
a  copper  negative  and  a  zinc  positive  plate.  The  copper  plate  is  immersed 
in  a  solution  of  copper  sulphate,  the  zinc  in  a  solution  of  zinc  sulphate  or 


FIG.  231. 


EXERCISES.  285 

dilute  sulphuric  acid,  and  a  porous  cup  separates  the  two  liquids.  By 
the  electrolytic  action  the  zinc  combines  with  the  sulphuric  acid  (H2S04), 
forming  zinc  sulphate  (ZnSO^,  thereby  setting  hydrogen  free.  This 
hydrogen,  while  on  its  way  to  the  negative  element  or  the  copper  plate, 
meets  the  copper  sulphate  solution  (CuSO*),  which  it  decomposes,  forming 
sulphuric  acid  again  (1X2804),  and  setting  free  the  copper,  which  is 
deposited  on  the  copper  plate. 


EXERCISES. 

1.  (a)  What  are  electrodes  ?     (6)  What  are  the  essential  parts  of  a 
voltaic  cell  ?     (c)  What  metal  is  almost  invariably  used  for  the  positive 
element  ?     (d)  Name  several  substances  that  are  quite  commonly  used 
for  the  negative  element,     (e)  What  happens  when  the  electrodes  are 
brought  in  contact  ?     (/)  What  purpose  does  joining  the  two  elements 
serve  ? 

2.  Why  ought  not  the  elements  of  a  voltaic  cell  to  touch  each  other  ? 

3.  What  is  the  function  of  a  voltaic  cell  ? 

4.  If  a  current  passes  points  A,  B,  C,  and  D  in  a  circuit  successively, 
(a)  which  point  is  positive  with  reference  to  all  the  others,  and  which 
point  is  negative  with  reference  to  all  the  others  ?     (6)  State  the  relation 
of  point  B  to  each  of  the  other  points. 

5.  With  what  propriety  is  the  zinc  element  of  a  voltaic  cell  called  the 
positive  element  and  the  negative  electrode  of  a  voltaic  system  ? 

6.  (a)  What  do  you  understand  by  the  "  polarization  of  the  negative 
element "  ?      (6)    How  is  it  caused  ?     (c)    What  harm  does  it  cause  ? 
(d)  How  is  it  commonly  prevented  ? 

7.  Which,  electricity  or  electrification,  is  the  result  of  work  done  ? 

8.  (a)  What  is  meant  by  "  local  action  "  ?     (6)  Why  is  it  objection- 
able ?     (c)  How  is  it  prevented  in  some  measure  in  certain  cells  ? 

9.  What  kind  of  cells  are  suitable  for  only  "  open  circuit  "  systems  ? 

10.  Which  of  the  several  cells  that  have  been  described  will  yield  a 
current  most  nearly  uniform  or  constant  ?     Why  ? 

11.  (a)  What  do  you  understand  by  an  open-circuit  battery  ?     (6) 
For  what  purposes   only  are  they  suited  ?     (c)  Which  of   the  several 
kinds  of  cells  that  have  been  described  is  especially  suited  for  closed- 
circuit  work  ? 

12.  Consult  technical  works   on    electricity  and  ascertain  how  the 
terms  "galvanic"  and  "voltaic"  became  associated  with  electro-chemi- 
cal cells. 


286 


ETHER    DYNAMICS. 


SECTION  II. 
EFFECTS    PRODUCIBLE    BY    AN    ELECTRIC    CURRENT. 

306.  Classification  of  Effects.      The   several   effects   pro- 
ducible by  an  electric  current  may  be  classified  as  electro- 
lytic, magnetic,  thermal,  and  physiological. 

307.  Electrolysis. 

Experiment  1.  Take  a  dilute  solution  of  sulphuric  acid  (1  part  by 
volume  to  10),  pour  some  of  it  into  the  funnel  (Fig.  232), 
so  as  to  fill  the  U-shaped  tube  when  the  stoppers  are 
removed.  Place  the  stoppers  which  support  the  plati- 
num electrodes  tightly  in  the  tubes.  Connect  with 
these  electrodes  the  battery  *  wires.  Instantly  bubbles 
of  gas  arise  from  both  electrodes,  accumulating  in  the 
upper  part  of  the  tube  and  forcing  the  liquid  back  into 
the  funnel.  Introduce  a  glowing  splinter  into  the  gas 
surrounding  the  +  electrode  :  it  relights  and  burns 
vigorously,  showing  that  the  gas  is  oxygen.  Invert 
the  glass  tube,  remove  the  rubber  tube,  allow  the 
gas  which  had  accumulated  about  the  —  electrode  to 
escape  at  A,  and  apply  a  lighted  match  to  it :  the  gas 
burns  ;  it*  is  hydrogen.  , 


FIG.  232. 


The  volume  of  hydrogen  is  just  double  that  of  the  oxygen 
liberated  in  the  same  time.  The  process  by  which  a  com- 
pound substance  is  separated  into  its  constituents  by  an 
electric  current  is  called  electrolysis,  and  a  compound  that  may 
be  thus  decomposed  is  called  an  electrolyte.  The  electrode  by 
which  the  current  enters  the  electrolyte  is  called  the  anode, 
and  that  by  which  the  current  leaves,  the  cathode.  Those 
constituents  that  appear  at  the  anodes  are  called  anions ; 
those  that  appear  at  the  cathodes  are  called  cations.  Anions 
are  electro-negative  and  cations  are  electro-positive  ;  hence, 
they  are  attracted  to  electrodes  that  are  oppositely  electrified. 


1  A  battery  consisting  of  not  less  than  two  Grenet  or  Bunsen  cells  connected  in 
series  will  be  required. 


MAGNETIZING   EFFECT    OF    ELECTRIC    CURRENT.     287 

Thus,  the  anion  oxygen,  being  electro-negative,  is  attracted  to 
the  anode,  or  positive  electrode,  and  the  cation  hydrogen, 
being  electro-positive,  is  attracted  to  the  cathode,  or  negative 
electrode. 

When  a  chemical  salt  is  electrolyzed,  the  base  appears  at  the  cathode, 
and  the  acid  at  the  anode.  In  general,  it  will  be  found  that  in  both  the 
battery  and  the  decomposing  cell,  hydrogen,  bases,  and  metals  appear  at 
the  plates  toward  which  the  current  flows. 

Experiment  2.  Prepare  a  solution  of  potassium  iodide.  Make  a  paste 
by  boiling  pulverized  starch  in  water. 
Take  a  small  portion  of  this  paste  and 
stir  it  into  the  solution.  Wet  a  piece 
of  writing-paper  with  the  liquid  thus 
prepared.  Spread  the  wet  paper 
smoothly  on  a  piece  of  tin,  e.g.  on 
the  bottom  of  a  tin  basin  (Fig.  233). 
Press  the  negative  electrode  of  the 
battery  (of  not  less  than  two  cells) 
against  an  uncovered  part  of  the  tin. 
Draw  the  positive  electrode  over  the  paper.  A  mark  is  produced  upon 
the  paper  as  if  the  electrode  were  wet  with  a  purple  ink.  In  this  case 
the  potassium  iodide  is  decomposed,  and  the  iodine  combining  with  the 
starch  forms  a  purplish-blue  compound. 

308.  Magnetizing  Effect  of  an  Electric  Current.  Electro- 
magnets. 

Experiment  3.  (a)  Wind  an  insulated  copper  wire  in  the  form  of  a 
spiral  round  a  rod  of  soft  iron  (Fig.  234).  Pass  a  current  of  electricity 
through  the  spiral,  and  hold  an  iron  nail  near  the  end  of  the  rod. 
Observe,  from  its  attraction  for  the  nail,  that  the  rod  is  magnetized.  A 
magnet  may  be  provisionally  defined  as  a  body  which  attracts  iron. 

(6)  Break  the  circuit ;  the  rod  loses  its  magnetism  and  the  nail  drops. 

The  iron  rod  is  called  a  core,  the  coil  of  wire  a  helix,  and 
both  together  are  called  an  electro-magnet.  In  order  to  take 
advantage  of  the  attraction  of  both  ends,  or  poles,  of  the 
magnet,  the  rod  is  frequently  bent  into  a  U-shape  (A,  Fig. 
235).  Often  two  iron  rods  are  nsed,  connected  by  a  rec- 


288 


DYNAMICS. 


tangular  piece  of  iron,  as  a  in  B  of  Fig.  235.  The  method 
of  winding  is  such  that  if  the  iron  core  of  the  U-magnet 
were  straightened,  or  the  two  spools  were 
placed  together  end  to  end,  one  would  appear 
as  a  continuation  of  the  other.  A  piece  of  soft 
iron,  b,  placed  across  the  ends  and  attracted  by 
them,  is  called  an  armature.  The  piece  of  iron 
a  is  called  a  yoke. 

309.  Deflection  of  the  Magnetic  Needle  by  a 
Current. 


FlG.  234. 


Experiment  4.  (a)  Place  the  apparatus  (Fig.  236)  so 
that  the  magnetic  needle,  which  points  (nearly)  north 
and  south,  shall  be  parallel  with  the  wires  Wi  and  W2.  Introduce  the 
+  electrode  of  a  battery  into  screw-cup  Tg  and  the  —  electrode  into 
screw-cup  TI,  and  pass  a  current 
through  the  upper  wire.  At  the 
instant  the  circuit  is  closed  the 


FIG.  235. 


needle  swings  on  its  axis,  and  after 
a  few  oscillations  comes  to  rest  in 
a  position  which  forms  an  angle 
with  the  wire  bearing  the  current. 

(6)  Break  the  circuit  by  removing  one  of  the  wires  from  the  screw- 
cup.      The  needle,  under  the  influence  of  the  magnetic  action  of  the 

earth,  returns  to  its  original 
position. 

(c)  Reverse  the  current  by 
inserting  the  +  electrode  of 
the  battery  into  screw-cup  TI 
and  the  —  electrode  into  screw- 
cup  T2.  Again  there  is  a  de- 
flection of  the  needle,  but  the 
direction  of  the  deflection  is 


FIG.  236. 


reversed  ;  that  is,  the  north- 
pointing  pole  (N-pole),  which 
before  turned  to  the  west,  is  now  deflected  toward  the  east. 

(d)  Place  your  right  hand  above  the  wire,  with  the  palm  towards  the 
wire  and  with  the  fingers  pointing  in  the  same  direction  as  that  in  which 
the  current  is  flowing,  and  extend  your  thumb  at  right  angles  to  the 


DEFLECTION    OF    MAGNETIC    NEEDLE.  289 

direction  of  the  current  (Fig.  237).  You  observe  that  your  thumb  points 
in  the  same  direction  as  the  N-pole  of  the  needle  under  the  current- 
bearing  wire. 

(e)  Reverse  the  current  again  (so  that  it  shall  flow  northward),  place 
your  right  hand  as  before  (viz.  with  the  palm  towards  the  wire  and  with 
the  fingers  pointing  in  the  same  direction  as  the  current)  ;  your  out- 
stretched thumb  still  points  in  the  same  direction  as  the  N-pole  of  the 
needle. 

(/)  Introduce  the  +  electrode  of  the  battery  into  screw-cup  T3  and 
the  — •  electrode  into  screw-cup  T^,  so  that  the  current  shall  flow  north- 
ward under  the  needle.  Place  the  right  hand  as  directed  before,  except 


FIG.  237.     Eight  hand  above  the  wire ;  FIG.  238.      Right  hand  below  the 

needle  below  it.  wire  ;  needle  above  it. 

that  it  must  be  under  the  wire,  so  that  the  wire  shall  be  between  the 
hand  and  the  needle  ;  the  thumb  will  point  in  the  same  direction  as  the 
N-pole  (Fig.  238).  Reverse  the  direction  of  the  current  in  this  wire,  and 
apply  the  same  test ;  the  same  rule  holds. 

The  rule  for  determining  the  direction  of  the  deflection  of 
the  N-pole  of  a  needle  when  the  direction  of  the  current  is 
known  is  this  :  Place  the  outstretched  right  hand  over  or  under 
the  wire,  so  that  the  wire  shall  be  between  the  hand  and  the 
needle,  with  the  palm  towards  the  needle,  the  fingers  pointing 
in  the  direction  of  the  current,  and  the  thumb  extended  laterally 
at  right  angles  to  the  direction  of  the  current ;  then  the  extended 
thumb  will  point  in  the  direction  of  the  deflection  of  the  N-pole. 

It  will  be  observed  that  a  deflection  is  reversed  either  by 
reversing  the  current  or  by  changing  the  relative  positions  of 
the  wire  and  needle,  e.g.  by  carrying  the  needle  from  above 
the  wire  to  a  position  below  it. 

The  force  exerted  by  the  current  upon  the  needle  in 
deflecting  it  is  called  an  electro-magnetic  force. 


290  ETHER   DYNAMICS. 

310.  Simple  Galvanoscope  or  Current  Detector. 

Experiment  5.  Introduce  the  4-  electrode  of  the  battery  into  screw- 
cup  TZ  (Fig.  236)  and  the  —  electrode  into  screw-cup  TS,  so  that  the 
current  shall  pass  above  the  wire  in  one  direction  and  below  it  in  the 
opposite  direction,  as  indicated  by  the  arrows.  A  larger  deflection  is 
obtained  than  when  the  current  passes  the  needle  only  once. 

If  the  right-hand  test  be  applied,  it  will  be  seen  that  the 
tendency  of  the  current,  both  when  passing  the  needle  in 
one  direction  above  and  in  the  opposite  direction  below,  is 
to  produce  a  deflection  in  the  same  direction,  and  conse- 
quently the  two  parts  of  the  current  assist  each  other  in 
producing  a  greater  deflection. 

If  a  more  sensitive  instrument,  i.e.  one  which  will  produce 
considerable  deflections  with  weak  currents,  be  required,  then 
it  will  be  necessary  to  pass  the  current  through  an  insulated 
wire  wound  many  times  around  the  needle.  Such  an  instru- 
ment is  called  a  galvanoscope,  or  current  detector,  since  one  of 
its  important  uses  is  to  detect  the  presence  of  a  current. 

311.  (3)   Thermal  and  Luminous  Effects    of   the  Electric 
Current. 

Experiment  6.  Construct  a  low  resistance  battery  (§  334)  of  three  or 
four  cells,  and  introduce  into  the  circuit  a  platinum  wire,  No.  30,  about 
i  inch  long.  The  wire  very  quickly  becomes  white  hot,  i.e.  it  emits 
white  light,  which  indicates  a  temperature  of  approximately  1900°  C. 

This  experiment  illustrates  the  conversion  of  the  energy 
of  an  electric  current  into  heat  energy.  In  this  case  the 
energy  of  the  current  is  consumed  in  overcoming  the  resist- 
ance which  the  conductor  or  the  circuit  offers  to  its  passage. 
Heat  is  developed  by  a  current  in  every  part  of  the  circuit, 
because  all  substances  offer  some  resistance  to  a  current  ;  in 
other  words,  there  are  no  perfect  conductors.  The  small 
platinum  wire  offers  much  greater  resistance  than  an  equal 
length  of  a  larger  copper  wire  ;  whence  the  greater  quantity 


STRENGTH    OF   CURRENT.  291 

of  heat  generated  in  this  part  of  the  circuit.  All  of  the 
energy  in  any  electric  current  that  is  not  consumed  in  doing 
other  kinds  of  work  is  changed  into  heat. 

312.  (4)  Physiological  Effects. 

Experiment  7.  Place  one  of  the  copper  electrodes  of  a  single  voltaic 
cell  on  each  side  of  the  tip  of  the  tongue.  A  slight  stinging  (not  painful) 
sensation  is  felt,  followed  by  a  peculiar  acrid  taste. 

EXERCISES. 

1.  (a)  Have  we  any  special  sense-organ  for  appreciating  electricity  ? 
(6)  Can  we  see  electricity  ? 

2.  What  distinction  do  you  make  between  an  electroscope  and  a 
galvanoscope  ? 

3.  Enumerate  the  various  effects  producible  by  an  electrical  current, 
and  give  in  connection  with  each  some  industrial  applications  to  which 
that  effect  gives  rise. 

4.  Are  any  of  the  effects  just  given  producible  by  electricity  when  in 
the  static  state  ? 

5.  Give  all  the  phenomena  with  which   you  are  familiar  that  are 
peculiar  to  electricity  in  the  statical  state. 

6.  (a)  Why  are  electrical   contacts  usually  made  of  platinum  ?     (6) 
Why,  in  electrolytical  experiments,  are  platinum  electrodes  usually  em- 
ployed ?     (c)  Why  will  not  platinum  electrodes  answer  for  the  decom- 
position of  chloride  salts?      [Carbon  electrodes  may  be  used  for  this 
purpose.] 

SECTION   III. 
ELECTRICAL   QUANTITIES    AND   UNITS.  —  OHM'S   LAW. 

313.  Strength  of  Current.    The  Ampere  and  the  Coulomb. 

The  magnitude  of  the  effects  produced  by  an  electric  current 
depends,  among  other  things,  upon  the  magnitude  of  the 
current.  Any  one  of  the  effects  producible  by  a  current 
may  be  made  the  basis  of  a  system  of  measurement  of 
currents.  For  example,  the  quantity  of  hydrogen  gas,  or  of 
any  metal  liberated  at  the  cathode  in  a  given  time  by  elec- 


292  ETHER   DYNAMICS. 

trolysis,  is  strictly  proportional  to  the  magnitude  of  the  cur- 
rent, or,  as  it  is  technically  termed,  the  strength  of  the  current. 
By  current  strength  is  meant  the  number  of  units  of 
electricity  which  flows  in  a  given  time,  or,  briefly,  the  "  rate 
of  flow."  The  practical  unit  of  current  strength  is  the  ampere. 
It  is  the  current  which,  passed  through  a  solution  of  nitrate  of 
silver  ("  in  accordance  with  standard  specifications  "),  deposits 
silver  at  the  rate  of  0.001118  gram  per  second.  The  quan- 
tity of  electricity  transferred  by  a  curfent  of  one  ampere  in 
one  second  is  called  a  coulomb.1  The  coulomb  is  the  unit  of 
quantity  of  electricity.  When  the  quantity  of  electricity  con- 
veyed by  a  current  in  one  second  is  one  coulomb,  its  strength 
is  one  ampere.  By  the  strength  of  a  current  is  meant  not  its 
total  flow  (which  would  be  expressed  in  coulombs),  but  a  rate  of 
flow,  and  this  distinction  should  be  borne  in  mind.2 

314.  Electro-motive  Force,  The  Volt.  Liquid  will  flow 
from  vessel  A  to  vessel  B  (Fig.  239),  provided 
the  pressure  be  greater  at  the  extremity  M 
of  the  pipe  C  than  at  the  extremity  N.  The 
difference  in  pressure  at  these  two  points  is 
proportional  to  the  "  head "  of  water  in  A, 
FIG.  239.  Qr  to  the  verticai  hight  D  E  of  the  liquid 

surface  in  A  above  the  liquid  surface  in  B.  We  might  say 
that  the  flow  of  liquid  is  due  to  a  liquid-motive  force  arising 
from  the  difference  of  pressure  at  the  points  M  and  N. 

1  The  definitions  of  the  coulomb  and  the  ampere  here  given  are  those  of  the  so- 
called  international  units,  which  were  adopted  as  the  legal  units  hy  act  of  the  United 
States  Congress  in  July,  1894. 

2  Roughly  expressed,  the  current  strength  employed  in  certain  practical  applica- 
tions is  as  follows  : 

In  electric  welding,  20  to  50  kilo-amperes. 
In  arc  lighting,  8  to  10  amperes. 

In  16  candle-power  incandescent  lamps,  .45  to  .75  ampere. 
In  average  telegraphic  circuit,  25  to  35  milliamperes. 
In  alternating  current  employed  in  the  execution  of  criminals  (New 
York  State),  3  to  8  amperes,  and  an  E.M.F.  of  about  1900  volts. 


ELECTRICAL  RESISTANCE.  293 

Similarly,  electricity  will  flow  in  a  conductor  provided 
there  be  what  may  be  termed  greater  electrical  pressure  at  one 
end  of  the  conductor  than  at  the  other  end.  As  long  as 
such  a  difference  of  pressure  is  maintained,  so  long  there  will 
exist  something  that  is  analogous  in  many  respects  to  a 
current-producing  force.  It  is  for  this  reason  called  electro- 
motive force  (E.  M.  F.).  Electro-motive  force  is  that  which 
maintains  or  tends  to  maintain  a  current  of  electricity  through 
a  conductor.  Like  a  mechanical  force,  it  has  a  definite  direc- 
tion. It  does  no  work  unless  it  moves  electricity. 

Difference  in  electrical  pressure  we  have  hitherto  assumed 
to  be  due  to  difference  of  potential.  Potential  difference  may 
be  due  to  contact  of  dissimilar  substances,  as  in  the  voltaic 
cell,  or  to  the  movement  of  a  part  of  the  conductor  in  a 
magnetic  field,  as  in  the  dynamo.  In  every  case  it  is  due 
to  an  expenditure  of  energy  of  some  kind. 

The  volt  is  the  name  chosen  for  the  practical  unit  of 
E.  M.  F.  and  difference  of  potential.  It  is  the  electrical  pres- 
sure required  to  maintain  a  current  of  one  ampere  against 
a  resistance  of  one  ohm  (§  315).  For  purposes  where  great 
accuracy  is  not  required,  it  will  answer  to  consider  a  volt  as 
the  E.  M.  F.  of  a  DanielFs  cell ;  i.e.  it  is  about  the  difference  of 
potential  between  the  zinc  and  copper  elements  of  this  cell, 
the  E.  M.  F.  of  a  standard  Daniell  cell  being  approximately 
1.07  volts. 

The  E.  M.  F.  which  causes  an  electric  spark  discharge  between  the 
brass  knobs  of  a  frictional  or  influence  machine  when  they  are  separated 
by  an  air  space  of  one  inch  may  be  as  high  as  75  kilo-volts. 

315,  Electrical  Resistance.  The  Ohm.  Every  substance 
offers  resistance  to  the  passage  of  a  current.  Those  substances 
which  offer  a  very  powerful  barrier  are  called  insulators.  The 
unit  of  resistance  is  called  the  ohm. 

The  international  ohm  is  "the  resistance  offered  to  an 
unvarying  electric  current  by  a  column  of  mercury  at  the 


294  ETHEfl   DYNAMICS 

temperature  of  melting  ice,  14.421  grams  in  mass,  of  a 
constant  cross-sectional  area,  and  of  the  length  of  106.3 
centimeters "  ;  or  about  the  resistance  of  9.3  ft.  of  No.  30 
(American  gauge)  copper  wire  (.01  in.  diam.). 

A  million  ohms  is  a  megohm  ;  a  millionth  of  an  ohm  is  a  microhm. 
The  resistance  of  a  cube  of  pure  water  of  1  cm.  edge  is  3.75  megohms ; 
i.e.  pure  water  is  almost  a  perfect  insulator. 

The  particular  resistance1  of  different  substances  referred  to  some 
standard  is  called  specific  resistance  or  resistivity1.  The  reciprocal  of 
resistivity  is  called  conductivity.  (See  Table  of  Resistivities  in  Appendix.) 

316.  Electrical  Power  and  Electrical  Work  or  Energy. 
When  an  electrical  current  of  one  ampere  flows  between  two 
points  in  a  conductor  whose  difference  of  potential  is  one 
volt,  work  is  done  at  the  expense  of  electrical  energy,  and 
heat  or  some  other  form  of  energy  is  generated  at  a  rate 
called  one  volt-ampere,  or  watt.  Briefly,  the  watt  is  the  rate  at 
which  work  is  done  in  a  circuit  where  the  electro-motive  force  is 
one  volt  and  the  current  is  one  ampere. 

If  a  coulomb  of  electricity  flow  between  two  points  in  a 
conductor  whose  difference  of  potential  is  one  volt,  a  quantity 
of  work  is  done,  or  a  quantity  of  electrical  energy  is  absorbed, 
that  is  called  a  volt-coulomb,  or  a  joule.  Briefly,  a  joule  is  the 
quantity  of  work  done  in  one  second  by  a  current  working  at  the 
rate  of  one  watt. 

The  watt  and  the  joule  are,  therefore,  units  of  electrical 
power  and  electrical  work  (or  energy),  respectively.      The 
volt-coulomb  or  joule  is  analogous  to  the  foot-pound,  and  in 
the  latitude  of  Washington,  D.C.V  is  equivalent  to  .738  ft.-lb. 
Watts  =  volts  X  amperes.     Joules  =  volts  X  coulombs.     Seven 
hundred  and  forty-six  watts  are  equivalent  to  one  horse-power. 
I  h.p.  =c=  0.746  kilowatt. 
1  k.w.=c=1.34h.p. 

1  The  termination  -ance  is  used  for  words  expressing  the  properties  of  a  body  ;  e.g. 
resistance,  conductance,  permeance,  etc.  The  termination  -ivity  or  -illty  is  used  for 
words  expressing  the  specific  properties  of  a  substance  ;  e.g.  resistivity,  conductivity, 
permeability,  etc. 


295 

317.  Resume,    A  unit  current  is  a  current  maintained  by  a 
unit  E.  M.  F.  against  a  unit  resistance. 

A  unit  E.  M.  F.  is  the  E.  M.  F.  required  to  maintain  a  unit 
current  against  a  unit  resistance. 

A  conductor  has  a  unit  resistance  when  a  unit  E.  M.  F.  (or 
a  unit  difference  of  potential  between  its  two  ends)  causes  a 
unit  current  to  pass  through  it. 

A  unit  of  electrical  power  is  the  power  of  a  unil;  current 
maintained  by  a  unit  difference  of  potential. 

A  unit  of  electrical  work  is  the  work  done  by  a  unit  current 
in  a  unit  time. 

318.  Ohm's  Law.     The  three  factors,  current  strength  ((7), 
electro-motive  force  (E),  and  resistance  (jft),  are  evidently 
interdependent.     Their  relations  to  one  another  are  stated  in 
the  well-known  Ohm's  law  thus  :  The  current  is  equal  to  the 
electro-motive  force  divided  by  the  resistance  ;  or, 

C  =  ^;  whence  E  =  R  (7,  and  R  =  ^ 
-K  C    , 

Hence,  the  strength  of  a  current  is  directly  proportional  to 
the  E.  M.  F.  and  inversely  proportional  to  the  resistance. 

If  E  represent  the  fall  of  potential,  R  the  resistance,  and  (7  the 
strength  of  current  between  any  two  points  in  a  circuit,  then  any  two  of 
the  three  quantities  being  given,  the  third  may  be  calculated. 

This  famous  law  is  the  basis  of  a  large  portion  of  electrical 
measurements  commonly  made. 

319.  Important  Laws.      The  following  formulas  and  laws 
relating  to  the  electric  current  will  be  found  convenient  for 
reference  :  (1)  P  (watts)  =  C  (amperes)  X  E  (volts).    (2)  The 

C*  T? 

watt  =c=  Ti^    horse-power.      Hence,  =— ^  =  power   in   horse- 
power.     (3)    Substituting   in    (1)   the   value   of    C    (Ohm's 

E'2 

formula),  we  have  P  =  —•     Or  (4),  substituting  in  (1)  the 
-K 

1  Resistance  is  often  defined  as  the  ratio  of  E.  M.  F.  to  the  current  strength. 


296  ETHrfR   DYNAMICS. 

value  of  E  (Ohm's  formula),  we  have  P  =  C2R ;  i.e.  power 
is  proportional  to  the  square  of  the  current  strength  when  R  is 
constant,  and  to  the  resistance  when  C  is  constant. 

The  number  of  units  of  heat  developed  in  a  conductor  is  pro- 
portional (1)  to  its  resistance,  (2)  to  the  square  of  the  strength 
of  the  current,  and  (3)  to  the  time  the  current  is  flowing. 

A  current  of  one  ampere  flowing  through  a  resistance  of 
one  ohm  develops  therein  0.00024  calorie  of  heat  per  second. 
Hence,  H  (calories)  =  C2  (amperes)  X  R  (ohms)  X  t  (seconds) 
X  0.00024. 

The  amount  of  chemical  decomposition  produced  by  a  current 
in  a  given  time  varies  as  the  strength  of  the  current.  On 
this  principle  is  based  the  voltameter,  which  measures  the 
strength  of  a  current  by  the  amount  of  chemical  action  it 
effects  in  a  given  time. 

The  mass  in  grams  of  an  element  deposited  by  electrolysis  is 
found  by  multiplying  its  electro-chemical  equivalent  (i.e.  the 
mass  in  grams  of  the  element  deposited  by  one  ampere  in 
one  second)  by  the  strength  of  the  current  in  amperes,  and  this 
product  by  the  time  in  seconds  during  which  the  current 
electrolyses. 

320.  Relation  of  Resistance,  Potential  Difference,  Current 
Strength,  and  Energy  Expended  in  an  Electric  Circuit, 
Deductions  from  Ohm's  Law. 

Let  the  line  A  B  (Fig.  240)  represent  the  length  of  a  circuit  (say 
1000  feet),  and  the  line  A  C  the  total  fall  of  potential ;  then,  obviously,  the 
slope  of  the  line  C  B  will  represent  the  average  rate  of  fall  of  potential 
throughout  the  circuit.  But  suppose  that  the  line  for  equal  lengths  of  the 
conductor  varies  in  resistance.  Thus,  assume  that  one  tenth  the  resist- 
ance and  consequently  one  tenth  the  fall  of  potential  (C  d)  is  included  in 
the  first  quarter  (A  a),  or  250  feet  ;  then  that  the  next  250  feet  (a  b,  being 
very  fine  wire,  perchance)  represents  one  half  the  total  resistance ;  that 
the  next  250  feet  (b  c)  represents  one  fourth  the  total  resistance  ;  and 
that  the  remaining  resistance,  fifteen  hundredths,  is  in  the  last  section 
(c  B)  of  250  feet.  Then  the  lines  C  a',  a'  b',  b'  c',  and  c'  B  represent, 
respectively,  the  rate  of  fall  of  potential  in  each  section  of  250  feet. 


EXERCISES. 


297 


The  above    is   a  deduction   from    Ohm's    law  ;    for,   since 

E 

C  =  — ,  and  C  is  the  same  in  every  section  of  the  conductor, 

it  follows  that  in  every  section  E  (fall  of  potential)  must  be 
proportional  to  R. 


Length  of  Conductor 
FIG. 240. 

Again,  since  the  power  consumed  or  work  performed  in 
any  circuit  is  proportional  to  the  resistance  when  the  cur- 
rent strength  is  constant  (formula  (4),  §  319),  and  since  the 
current  strength  is  the  same  in  every  section  of  the  circuit, 
it  follows  that  the  energy  expended  in  any  given  section  of  a 
circuit  is  proportional  to  the  resistance  of  the  section.  We 
conclude,  therefore,  that  the  fall  of  potential  along  a  con- 
ductor and  the  work  done  (or  energy  expended)  are  propor- 
tional to  the  resistance  encountered  in  the  different  parts  of  the 
conductor. 


EXERCISES. 

1.  What  E.  M.  F.  is  required  to  maintain  a  current  of  1   ampere 
against  a  resistance  of  1  ohm? 

2.  An  E.  M.  F.  of  10  volts  will  maintain  a  current  of  5   amperes 
against  what  resistance  ? 

3.  What  current  ought  an  E.  M.  F.  of  20  volts  to  maintain  against  a 
resistance  of  5  ohms  ? 

4.  A  voltmeter  applied  each  side  of  an  electric  lamp  shows  a  differ- 
ence of  potential  of  40  volts.    What  current  flows  through  the  lamp,  if  it 
have  a  resistance  of  10  ohms  ? 


r, 


298  ETHETR    DYNAMICS. 

5.  The  resistance  between  two  points  in  a  circuit  is  10  ohms.     An 
ammeter  (an  instrument  which  measures  the  strength   of  a  current  in 
amperes)  shows  that  there  is   a  current  strength   in  the  circuit  of  0.5 
ampere.     What  is  the  difference  in  potential  between  the  points  ? 

6.  (a)  If  150  coulombs  of  electricity  be  transferred  through  a  circuit 
in  30  seconds,  what  is  the  average  current  strength  ?     (6)  What  quantity 
of  electrical  work  is  done  ? 

7.  A   current  of  4  amperes  flows  5  minutes.     What  quantity  of 
electricity  is  transferred  ? 

8.  When  the  difference  of  potential  between  two  points  in  a  circuit  is 
80  volts  and  the  resistance  between  these  points  is  40  ohms,  what  quan- 
tity of  electricity  will  pass  between  the  points  in  1  minute  ? 

9.  (a)  Is  it  proper  to  speak  of  the  power  or  of  the  energy  of  an  elec- 
trical current  ?     (b)  Of  the  energy  or  of  the  power  absorbed  by  an  electric 
lamp  ?      (c)  Of  the  energy  or  of  the  power  absorbed  in  a  lamp  in  5 
minutes  ? 

10.  How  much  heat  is  generated  per  minute  in  a   16  candle-power 
electric  lamp  having  a  resistance  of  140  ohms  and  a  fall  of  potential  of 
110  volts,  when  a  current  of  .75  ampere  is  maintained  in  it  ? 

11.  The  electro-chemical  equivalent  of  copper  is  .000328  g.     If  in  a 
Daniell' s  cell  the  electro-negative  element  increased  .6  g.  in  25  minutes, 
what  was  the  average  current  strength  during  the  time  ? 

12.  A  current  of  40  amperes  is  sent  over  a  line  of  4  ohms  resistance. 
What  is  the  total  fall  of  potential  in  the  line  ? 

13.  If  200  coulombs  be  transferred  in  40  seconds,  what  is  the  average 
current  strength  ? 

SECTION  IV. 

INSTRUMENTS    FOR    MEASUREMENT    OF    ELECTRIC 
CURRENTS. 

321.  Galvanometer.  This  is  an  instrument  for  measuring 
current  strength  by  means  of  the  deflection  of  a  magnetic 
needle  when  placed  in  the  field  of  the  current.  It  is  so  con- 
structed that  either  the  deflection  angle  itself,  or  some  func- 
tion of  it,  is  proportional  to  the  current  strength. 

A  very  simple  form  of  this  instrument  is  represented  in  sectional 
elevation  and  plan  in  Fig.  241.  It  consists  of  an  insulated  wire  wound 
many  times  around  a  magnetic  needle.  A  card  graduated  like  that  of  a 
mariner's  compass  is  placed  beneath  the  needle  so  that  the  number  of 


GALVANOMETERS. 


299 


GALVANOMETER  COIL 


degrees  of  deflection  may  be  read  from  it.     This  form  of  instrument  is 
much  used  to  detect  the  presence  of 
a  current,  to  locate  faults,  etc. 

322.  Tangent  Galvanometer. 

A  tangent  galvanometer  is  one 
so  constructed  that  the  current 
passing  through  it  is  propor- 
tional to  the  tangent  of  the 
angle  of  deflection  produced. 
To  this  end  it  is  necessary  that 
the  needle  be  very  short  (not 
more  than  ^)  in  comparison 
with  the  diameter  of  the  coil. 
It  consists  of  a  large  vertical 
coil  (C,  Fig.  242)  in  the  center 
of  which  is  either  a  small  compass  needle  or  a  needle  sus- 
pended by  a  silk  fiber.  A  needle  thus  placed  in  the  field  of 

a  current  is  acted  on  by  a  mechanical 
couple  tending  to  place  it  at  right 
angles  to  the  plane  of  the  coil,  and 
is  deflected  until  it  is  balanced  by 
the  opposing  couple  due  to  the  earth's 
magnetism. 

When  the  scale  is  divided  into 
degrees,  the  corresponding  tangents 
are  found  by  consulting  a  table  of 
tangents.  (See  Appendix).  When 
the  strengths  of  two  currents  are  to 
be  compared,  it  is  only  necessary  to 
obtain  deflections  with  each  current, 
and  compare  the  tangents  of  the 
angles. 


FIG.  242. 


323.  Ammeter.     If  the  galvanometer  be  calibrated  so  as  to 
read  in  amperes,  we  shall  have  a  direct-reading  ampere-meter, 


300  ETHER    DYNAMICS. 

or  ammeter,  as  it  is  more  commonly  called.  There  is  a  great 
variety  of  ammeters  in  use,  for  a  description  of  which  the 
student  is  referred  to  technical  works  on  the  subject. 

EXERCISES. 

1.  (a)  Compare  the  strengths  of  two  currents  which  produce  deflec- 
tions in  a  tangent  galvanometer  of  10°  and  5°,  respectively.     (6)   Of  87° 
and  88°.     (c)  In  which  of  the  two  cases  are  the  current  strengths  more 
nearly  proportional  to  the  angles  of  deflection  ? 

2.  The  tendency  of  an  electric  current  is  to  place  a  magnetic  needle 
at  right  angles  to  itself.     Why  does  the  needle  never  quite  attain  this 
angle  ? 

3.  (a)  What  is  an  ammeter  ?     (6)  How  can  a  galvanometer  be  con- 
verted into  an  ammeter  ?     (c)  Does  a  galvanometer  measure  the  strength 
of  a  current  directly  ? 

SECTION  V. 
RESISTANCE   OF    CONDUCTORS. 

324.  External  and  Internal  Resistance.  For  convenience 
the  resistance  of  an  electric  circuit  is  divided  into  two  parts, 
the  eosterma^  and  the  internal.  External  resistance  includes 
all  the  resistance  of  a  circuit  except  that  of  the  generator, 
while  that  of  the  latter  is  termed  internal  resistance. 

When  the  external  resistance  in  a  circuit  is  considered 
separately  from  the  internal,  Ohm's  formula  must  be  con- 
verted thus  (calling  the  former  R,  and  the  latter  r)  : 

c-    E 

-R+~r 

If  the  electrical  dimensions  of  a  cell  be  E  —  1  volt,  and  r  = 
1  ohm,  and  the  connecting  wire  be  short  and  stout,  so  that  R 
may  be  disregarded,  then  the  cell  yields  a  current  of  one 
ampere.  If  by  any  means  the  internal  resistance  of  this  cell 
can  be  decreased  one  half,  it  will  then  be  capable  of  yielding 
a  two-ampere  current  if  the  other  conditions  remain  the 
same. 


EXPERIMENTS. 


301 


325,  External  Resistance. 

Experiment  1.  Introduce  into  a  circuit  a  galvanometer,  and  note  the 
number  of  degrees  the  needle  is  deflected.  Then  introduce  into  the 
same  circuit  the  wire  on  the  spool  numbered  4  on  the  platform *  S  (Fig. 
243).  (The  wire  on  any  one  of  the  five  spools  on  this  platform  can  at 
any  time  be  introduced  into  a  circuit  by  connecting  the  battery  wires 
with  the  binding  screws  on  each  side  of  the  spool  to  be  introduced.) 


FIG.  243. 

The  deflection  is  now  less  than  before.  The  copper  wire  on  this  spool 
is  16  yards  in  length  ;  its  size  is  No.  30  of  the  Brown  and  Sharpe  wire 
gauge.  When  this  spool  is  in  circuit,  the  circuit  is  16  yards  longer  than 
when  the  spool  is  out.  The  effect  of  lengthening  the  circuit  is  to  weaken 
the  current,  as  shown  by  the  diminished  deflection. 

Experiment  2.  Next,  substitute  Spool  2  for  Spool  4.  This  contains 
32  yards  of  the  same  kind  of  wire  as  that  on  Spool  4.  The  deflection  is 
still  smaller. 

The  weakening  of  the  current  by  introducing  these  wires  is  caused  by 
the  resistance  which  the  wires  offer  to  the  current,  much  as  the  friction 
between  water  and  the  interior  of  a  pipe  impedes,  to  some  extent,  the 
flow  of  water  through  it.  The  longer  the  pipe  the  greater  is  the  resistance 
to  the  flow. 

If  the  wire  on  the  spools  had  been  the  only  resistance  in  the  circuit, 
then,  when  Spool  2  was  in  the  circuit,  the  resistance  would  have  been 
double  what  it  was  when  Spool  4  was  in  the  circuit,  and  the  current,  with 
double  the  resistance,  would  have  been  half  as  strong. 

(1)  Other  things  being  equal,  the  resistance  of  a  conductor 
varies  as  its  length. 

1  A  platform  of  spools  containing  wire  of  different  (known)  sizes,  lengths,  and 
material,  so  arranged  that  any  one,  two,  or  more  can  be  introduced  into  the  circuit. 


302  ETH1&,   DYNAMICS. 

Experiment  3.  Next  substitute  Spool  1  for  Spool  2.  This  spool  con- 
tains 32  yards  of  No.  23  copper  wire, —  a  thicker  wire  than  that  on  Spool 
2, —  but  the  length  of  the  wire  is  the  same.  The  deflection  is  now 
greater  than  it  was  when  Spool  2  was  in  circuit.  This  indicates  that  the 
larger  wire  offers  less  resistance. 

Careful  experiments  show  that  (2)  the  resistance  of  all  con- 
ductors varies  inversely  as  the  areas  of  their  cross  sections.  If 
the  conductors  be  cylindrical,  it  varies  inversely  as  the  squares 
of  their  diameters. 

Experiment  4.  Substitute  Spool  5  for  Spool  1,  and  compare  the  deflec- 
tion with  that  obtained  when  Spool  4  was  in  the  circuit.  The  deflection 
is  smaller  than  when  Spool  4  was  in  circuit.  The  wire  on  these  two  spools 
is  of  the  same  length  and  size,  but  the  wire  of  Spool  5  is  German  silver. 
It  thus  appears  that  German  silver  offers  more  resistance  than  copper. 

(3)  In  obtaining  the  resistance  of  a  conductor,  the  specific 
resistance  of  the  substance  must  enter  into  the  calculation.    (See 
Table  of  Specific  Resistances  in  the  Appendix.) 

The  resistance  of  metal  conductors  increases  slowly  with  a 
rise  of  temperature  of  the  conductor.  The  resistance  of  Ger- 
man silver  is  affected  less  by  changes  of  temperature  than 
that  of  most  metals  ;  hence  its  general  use  in  standards  of 
resistance.  The  resistance  of  carbon  diminishes  with  a  rise 
of  temperature.  The  resistance  of  carbons  in  electric  lamps 
is  less  when  hot  than  when  cold. 

326.  Internal  Resistance. 

Experiment  5.  Connect  with  the  galvanometer  the  copper  and  zinc 
strips  used  in  Experiment  1,  Section  1,  and  introduce  the  strips  into  a 
tumbler  nearly  full  of  acidulated  water.  Note  the  deflection.  Then 
raise  the  strips,  keeping  them  the  same  distance  apart,  so  that  less  and 
less  of  the  strips  will  be  submerged.  As  the  strips  are  raised,  the  de- 
flection becomes  smaller.  This  is  caused  by  the  increase  of  resistance  in 
the  liquid  part  of  the  circuit,  as  the  cross  section  of  the  liquid  lying 
between  the  two  strips  becomes  smaller. 

(4)  The  internal  resistance  of  a  circuit,  other  things  being 
equal,  varies  inversely  as  the  area  of  the  cross  section  of  the 
liquid  between  the  two  elements. 


THE    RESISTANCE   BOX.  303 

In  a  large  cell  the  area  of  the  cross  se'ction  of  the  liquid 
between  the  elements  is  larger  than  in  a  small  cell,  and  con- 
sequently the  internal  resistance  is  less.  This  is  the  only 
way  in  which  the  size  of  the  cell  affects  the  current. 

Obviously,  the  resistance  of  the  battery  would  be  increased  by  any  in- 
crease of  the  distance  between  the  elements,  since  this  increases  the  length 
of  the  liquid  conductor  ;  but  as  this  distance  is  usually  made  as  small  as 
convenient,  and  is  kept  invariable,  it  demands  little  of  our  attention. 

EXERCISES. 

1.  The  resistance  of  1000  feet  of  No.  24  copper  wire  (diameter  = 
.511  mm.)  is  26.284   ohms.     What  length  of  this  wire  would  have  a 
resistance  of  .5  ohm  ? 

2.  What  is  the  resistance  of  100  feet  of  No.  30  copper  wire  (diameter 
=  .255  mm.)  ? 

3.  What  is  the  resistance  of  30  feet  of  No.  30  German-silver  wire  (the 
resistance  of  copper  and  German  silver  being  as  1  : 12.8)  ? 


SECTION   VI. 
MEASUREMENT   OF   RESISTANCE. 

327.  Description  of  the  Resistance  Box. 

Fig.  244  represents  a  cylindrical  box  containing  a  series  of  coils 
of  German-silver  wire,  whose  resistances 
range  from  0.1  ohm  to  50  ohms,  so  that 
the  total  resistance  is  160  ohms.  These 
coils  consist  of  insulated  and  doubled 
wires,  the  terminals  of  each  being  con- 
nected with  brass  blocks  A,  B,  C,  etc. 
(Fig.  245).  When  the  brass  plugs  1,2, 
etc.,  are  inserted  between  these  blocks,  the 
coils  are  short  circuited,  so  that  practically 
the  whole  current  passes  through  the  plugs 
from  block  to  block  ;  but  when  a  plug  is 
withdrawn  the  current  is  obliged  to  trav- 
erse the  corresponding  coil.  Thus,  by  FIG.  244. 
withdrawing  the  proper  plugs,  any  desired  resistance  within  the  capacity 


304 


ETHER    DYNAMICS. 


of  the  box  may  be  thrown  into  the  circuit.  The  resistance  box  is  intro- 
duced into  the  circuit  by  connecting  the  battery 
terminals  with  the  screw-cups  A  and  B  (Fig.  244). 


328.  Wheatstone  Bridge. 

Fig.  246  represents  a  perspective  view  of  the 
bridge  (as  modified  by  the  author),  and  Fig.  247 
FIG.  245.  represents  a  diagram   of  the  essential   electri- 

cal connections.  The  battery  wires  are  connected  with  the  bridge  at 
the  binding  screws  B  B'.  A  galvanometer,  G",  is  connected  at  G  G',  a 
resistance  box,  r,  at  R  R,  and 
the  conductor,  x,  whose  resist- 
ance is  sought,  at  X  X. 

When  the  circuit  is  closed 
by  means  of  the  key  T,  the 
current,  we  will  suppose,  enters 
at  B  ;  on  reaching  the  point  A 
it  divides,  one  part  flowing  via 
the  branch  A  G  B',  and  the  other 

via  the  branch  A  D  B'.     If  points  D  and  G  in  the  two  branches  be  at  dif- 
ferent potentials  and  a  connection  be  made  between  them  through  the 

galvanometer  G',  by  closing 
the  key  S  there  will  be  a 
current  through  this  wire  and 
through  the  galvanometer, 
and  a  deflection  of  the  needle 
will  be  produced.  But  if  the 
points  D  and  G  have  the  same 
potential,  there  will  be  no 
cross  current  through  the 
bridge  wire  and  no  deflection. 
In  §  320  it  was  demonstrated 
that  the  fall  of  potential  along 
a  circuit  is  everywhere  pro- 
portional  to  the  resistance. 
If,  therefore,  we  have  a  di- 
vided circuit(§  331),  consisting 
of  two  branches,  A  G  B'  and 
A  D  B'  (Fig.  247),  of  any  resistance  whatever,  and  if  we  select  points  G 
and  D  so  that  the  resistance  on  both  sides  of  them  in  each  branch  are  in 
the  proportion  A  G  :  G  B'  =  A  D  :  D  B',  then  the  fall  of  potential  through 
A  G  will  be  the  same  as  that  through  A  D  and  there  will  be  no  difference 


WHEATSTONE    BRIDGE.  305 

of  potential  between  G  and  D,  and  there  will  be  no  flow  of  current 
through  the  bridge  G  D  and  galvanometer  G",  however  large  a  current 
may  be  flowing  through  the  divided  circuit.  Between  A  and  D,  and  A  and 
G,  there  are  three  coils  of  wire  having  resistances,  respectively,  of  1,  10, 
and  100  ohms.  One  or  more  of  these  coils  are  introduced  into  the  circuit 
by  removing  the  corresponding  plugs  a,  b,  c,  d,  e,  and  f.  As  the  other 
connections  between  A  and  D,  and  A  and  G,  have  no  appreciable  resistance, 
being  for  the  most  part  short  brass  bars,  the  only  practical  resistance 
between  these  points  is  that  introduced  at  will  through  the  coils.  Sim- 
ilarly, between  points  D  and  B7  the  only  practical  resistance  is  that  intro- 
duced at  will  through  the  resistance  box,  and  between  the  points  G  and 
B'  the  resistance  is  the  resistance  (x)  sought. 

It  is  apparent,  then,  that  in  using  the  bridge  after  the  connections  are 
properly  made  through  the  several  instruments  and  certain  known 
resistances  are  introduced  between  A  and  D  and  A  and  G,  we  have  sim- 
ply to  regulate  the  resistance  through  the  resistance  box  so  that  there 
will  be  no  deflection  in  the  galvanometer  ;  jthen  we  are  sure  that  the 
above  proportion  is  trtfe.  The  firsfc'three  terms  of  the  proportion  being 
known,  the  fourth  tern;,  which  is  the  resistance  sought,  is  computable.1 

If  the  same  resistance  be  introduced  between  points  A  and  G  as 
between  A  and  D,  it  is  evident  that  the  resistance  in  the  resistance  box  r 
must  be  made  equal  to  the  unknown  resistance  x  in  order  that  there  may 
be  no  deflection  in  the  galvanometer.  Consequently,  when  this  result  is 
obtained,  the  resistance  of  x  may  be  read  from  the  resistance  box. 

Experiment.  Measure  the  resistance  of  each  of  the  several  spools  of 
wire  used  above,  electro-magnets,  electric  lamps,  etc.,  using  the  bridge. 
Place  the  switches  of  the  resistance  box  on  the  zero  studs.  Make  con- 
nections as  in  the  description  above.  Then  close  the  circuit  at  T,  and 
afterwards  the  bridge  at  S.  There  will  probably  be  a  deflection  in  the 
galvanometer.  Regulate  the  resistance  through  the  resistance  box, 
throwing  in  or  taking  out  resistance  according  as  one  or  the  other  tends 
to  reduce  the  deflection  (the  process  is  much  like  that  of  weighing),  until 
there  is  no  deflection.  Then  compute  the  resistance  sought  according  to 
the  above  proportion. 

1  The  accuracy  of  the  results  obtained  largely  depends  upon  so  choosing  resist- 
ances of  the  bridge  as  to  make  the  arrangement  have  maximum  sensibility,  and  upon 
the  sensitiveness  of  the  galvanometer.  In  using  the  bridge  the  following  directions 
should  be  observed  :  (1)  Always  close  the  circuit  at  T  before  closing  the  bridge  at  S, 
and  in  breaking  the  circuit  reverse  this  order.  (2)  Introduce  between  A  and  D  and 
A  and  G  resistance  as  nearly  equal  to  the  resistance  sought  (x)  as  practicable.  If 
you  have  no  conception  what  the  unknown  resistance  is,  it  is  best  to  begin  by  using 
high  resistances.  (3)  Use  a  sensitive  galvanometer,  e  g.  a  mirror  galvanometer,  or 
the  galvanometer  shown  in  Fig.  243,  substituting  the  astatic  needle  for  the  tangent 
needle. 


306 


ETHER    DYNAMICS. 


329,     Measurement 


of    Galvanometer    Resistance. 
Kelvin's  Method. 


Lord 


The  bridge  may  be  used  for  measuring 
the  resistance  of  the  galvanometer  actually 
in  use.  The  bridge  is  arranged  as  in  Fig. 
248.  The  resistance  in  the  resistance  box 
R  is  then  varied  until  the  deflection  in  G 
does  not  change  when  the  key  S  is  closed  ; 
then 

_  a 
r=R-, 

in  which  r  is  the  resistance  of  the  galva- 
nometer, R  is  the  resistance  in  the  resistance 
box,  and  a  and  b  are  the  resistances  in  the 
arms  A  G'  and  A  D,  respectively.  If  a  =  6, 
then  r  =  R. 


J 


SECTION   VII. 

E.M.F.    OF    DIFFERENT    CELLS.      DIVIDED    CIRCUITS. 
METHODS    OF   COMBINING   VOLTAIC    CELLS. 


330.  Electro-motive  Force  of  Different  Cells.  If  a  galva- 
nometer be  introduced  into  a  circuit  with  different  battery 
cells,  e.g.  Bunsen,  Daniell,  Grenet,  etc.,  very  different  deflec- 
tions will  be  obtained,  showing  that  the  different  cells  yield 
currents  of  different  strengths.  This  may  be  in  some  measure 
due  to  a  difference  in  their  internal  resistances,  but  it  is  chiefly 
due  to  the  difference  in  their  electro-motive  forces.  We  have 
learned  that  difference  of  electro-motive  force  is  due  to  the 
difference  of  the  chemical  action  on  the  two  plates  used,  and 
this  depends  upon  the  nature  of  the  substances  used.  It  is 
wholly  independent  of  the  size  of  the  plates  ;  hence,  the 
electro-motive  force  of  a  large  cell  is  no  greater  than  that  of 
a  small  one  of  the  same  kind.  Consequently,  any  difference 
in  strength  of  current  yielded  by  cells  of  the  same  kind,  but  of 


LORD    KELVIN. 


DIVIDED    CIRCUITS.  307 

different  sizes,  is  due  wholly  to  a  difference  in  their  internal 
resistances. 

The  electro-motive  forces  of  the  Bunsen,  Daniell,  and 
Grenet  cells  are,  respectively,  about  1.8,  1,  and  2  volts. 

331.  Divided  Circuits ;  Shunts. 

Experiment.  Make  a  divided  circuit  as  in  Fig.  249  (using  double 
connectors  a  and  b).  Insert  a  galvanometer,  G,  in  one  branch  and  a 
resistance  box,  R,  in  the  other.  When  the  current  reaches  a,  it  divides, 
a  portion  traversing  one  branch  through  the  galvanom- 
eter, and  the  remainder  passing  through  the  other  branch 
and  the  resistance  box.  The  branch  a  R  b  is  called  a 
shunt  or  derived  circuit.  Increase  gradually  the  resist- 
ance in  the  resistance  box.  The  result  is  that  it  throws 
more  of  the  current  through  the  galvanometer,  as  shown 
by  the  increase  of  deflection. 

In  a  divided  circuit  the  current  is  distributed 
between  the  paths  in  amounts  inversely  as  their 
resistances.     For  example,  if  the  resistance  of  the  resistance 
box  above  be  4  ohms,  and  the  resistance  in  the  galvanometer 
be  1  ohm,  then  four  fifths  of  the  current  will  traverse  the 
latter  and  one  fifth  the  former. 

Suppose  that  the  resistance  box  and  galvanometer  be 
removed  from  the  shunts,  and  that  the  shunts  be  of  the 
same  length,  size,  and  kind  of  wire,  and  consequently  have 
equal  resistances,  then  using  the  two  wires  instead  of  one  to 
connect  a  and  b  is  equivalent  to  doubling  the  size  of  this 
portion  of  the  conductor ;  consequently,  the  resistance  of  this 
portion  is  reduced  one  half. 

Generally,  the  joint  resistance  of  two  branches  of  a  circuit  is 
the  product  of  their  respective  resistances  divided  by  their  sum. 

If  any  portion  of  a  circuit  be  divided  into  three  or  more 
branches  whose  resistances  are,  respectively,  r1?  r2,  r8,  etc., 
it  may  be  demonstrated  x  that 

1  See  the  author's  "  Principles  of  Physics,"  p.  509. 


308  ETHEft    DYNAMICS. 

in  which  R  represents  the  joint  resistance  of  the  several 
branches.  That  is,  the  reciprocal  of  the  joint  resistance  of 
any  number  of  branches  is  equal  to  the  sum  of  the  reciprocals 
of  the  resistances  of  the  several  branches. 

The  reciprocal  of  the  resistance  E  of  a  wire,  i.e.  — ,  is  called  its  con- 
ductance (sometimes  expressed  in  a  unit  called  the  mho 1).  We  may  say, 
therefore,  in  general,  that  when  two  points  in  a  circuit  are  connected  by 
a  multiple  arc  (a  term  hi  common  use  to  denote  a  divided  circuit  between 
any  two  points)  consisting  of  n  branches,  the  conductance  of  the  multiple 
arc  is  equal  to  the  sum  of  the  conductances  of  the  n  branches. 

332.  Shunted  Galvanometers.     When   it   is    necessary   to 
measure  a  current   that   exceeds   the   capacity  of   a   galva- 
nometer, a  wire  may  be  connected  across  the  terminals  of 
the  galvanometer,  by  means  of  which  any  fraction  of  the  cur- 
rent may  be  deflected,  and  the  galvanometer  then  measures  a 
known  fraction  of  the  total  current. 

For  example,  if  the  resistance  of  the  galvanometer  be  3  ohms  and  the 
resistance  of  the  shunt  be  (^  of  3  =  )  .33  ohm,  then  the  current  in  the 
galvanometer  will  be  £  of  the  current  in  the  shunt,  or  ^  of  the  total 
current. 

333.  Combining  Cells;  Batteries. 

A  number  of  cells  connected  in  such  a  manner  that  the 
currents  generated  by  all  have  the  same  direction  constitutes 
a  voltaic  battery.  The  object  of  combining  cells  is  to  get  a 
stronger  current  than  one  cell  will  afford.  We  learn  from 
Ohm's  law  that  there  are  two,  and  only  two,  ways  of  increas- 
ing the  strength  of  a  current.  It  must  be  done  either  by 
increasing  the  E.  M.  F.  or  by  decreasing  the  resistance.  So  we 
combine  cells  into  batteries,  either  to  secure  greater  E.  M.  F. 
or  to  diminish  the  internal  resistance.  Unfortunately,  both 
purposes  cannot  be  accomplished  by  the  same  method. 

1 A  word  formed  by  writing  the  word  ohm  in  reverse  order. 


INTERNAL    RESISTANCE    OF    BATTERIES. 


309 


334.  Batteries  of  Low  Internal  Resistance.  Figure  250 
represents  three  cells  having  all  the  carbon  (+) 
plates  electrically  connected  with  one  another, 
and  all  the  zinc  (—  )  plates  connected  with  one 
another,  and  the  triplet  carbons  connected  with 
the  triplet  zincs  by  the  leading-out  wires  through 
a  galvanometer,  G. 

It  is  easy  to  see  that  through  the  battery  the 
circuit  is  divided  into  three  parts,  and  conse- 
quently the  conductance  in  this  part  of  the  cir- 
cuit, according  to  the  principle  stated  in  §331, 
must  be  increased  threefold  ;  in  other  words,  the 
internal  resistance  of  the  three  cells  is  one  third 
of  that  of  a  single  cell.  This  is  called  connecting 
cells  "in  multiple  arc/'  and  the  battery  is  called 
a  "battery  of  low  internal  resistance."  The  re- 
sistance of  the  battery  is  decreased  as  many  times 
as  there  are  cells  connected  in  multiple  arc,  but 
the  E.  M.  F.  is  that  of  one  cell  only. 

The  formula  for  the  current  strength  in  this  case  is  written 
thus: 


FIG.  250. 


in  which  n  represents  the  number  of  cells.      It  is  evident 

from  this  formula  that  when  R  is  so  great  that  -  is  a  small 

n 

part  of  the  whole  resistance  of  the  circuit,  little  is  added  to 
the  value  of  C  by  increasing  the  number  of  cells  in  multiple 
arc. 

335.  Batteries  of  High  Internal  Resistance  and  Great  E.  M.  F. 

Fig.  251  represents  four  cells  having  the  carbon  or  —  plate 
of  one  connected  with  the  zinc  or  +  plate  of  the  next,  and 
the  +  plate  at  one  end  of  the  series  connected  by  leading-out 


310  ETHER*  DYNAMICS. 

wires  through  a  galvanometer  with  the  —  plate  at  the  other 
end  of   the  series.     It  is  evident  that  the  current  in  this 

series  traverses  the  liquid  four 
times,  which  is  equivalent  to 
lengthening  the  liquid  con- 
ductor four  times,  and  of 
course  increasing  the  inter- 
nal resistance  fourfold.  But, 
while  the  internal  resistance 
is  increased,  the  E.  M.  F.  of 
the  battery  is  increased  as  many  times  as  there  are  cells  in  series. 
In  many  cases  (always  when  the  internal  resistance  is  a 
small  part  of  the  whole  resistance  of  the  circuit)  the  gain  by 
increasing  the  E.  M.  F.  more  than  offsets  the  loss  occasioned 
by  increased  resistance. 

The  formula  for  current  strength  in  this  case  becomes 


E  -t-  nr 

It  is  evident  that  C  is  increased  most  by  adding  cells  in 
series  when  n  r  is  smallest  in  comparison  with  K 

336.  Rule  for  Combining  Cells. 

When  the  external  resistance  is  large,  connect  cells  in  series; 
when  the  external  is  less  than  the  internal  resistance,  connect 
cells  in  multiple 


EXERCISES. 

1.  What  E.  M.  F.  is  required  to  maintain  a  current   of  .2  ampere 
through  a  resistance  of  .8  ohm  ? 

2.  Through  what  resistance  will  an  E.  M.  F.  of  10  volts  maintain  a 
current  of  9  amperes  ? 

3.  What  current  ought  an  E.  M.  F.  of  85  volts  to  maintain  through  a 
resistance  of  8  ohms  ? 

4.  A  voltmeter  (Fig.  252)  applied  each  side  of  an  electric  lamp  shows 
a  difference  of  potential  of  10  volts.    What  current  fjow$  through  the 
lamp,  if  it  have  a  resistance  of  50  ohms  ? 


EXERCISES. 


311 


5.  The  resistance  between  two  points  in  a  circuit  is  70  ohms.     An 
ammeter  shows  that  there  is  a  current  strength  in  the  circuit  of  0.5 
ampere.     What  is  the  difference  in 

potential  between  the  points  ? 

6.  What  current  will  a  Bunsen 
cell  furnish  when  r  —  0.9  ohm  (about 
the  resistance  of  a  quart  cell),  E  —  1.8 
volts,  and  R  =  0.01  ohm  (about  the 
resistance  of  3  feet  of  No.  16  wire)  ? 

[In  the  following  exercises,  when- 
ever a  Bunsen  cell  is  mentioned  it 
may  be  understood  to  be  a  quart 
cell,  having  a  resistance  of  about  0.9 
ohm.  Its  E.  M.  F.  is  about  1.8  volts.] 

7.  (a)  When  is  a  large  cell  con- 
siderably better  than  a  small  one  ? 

(b)  When  does  the  size  of  the  cell  make  little  difference  in  the  current  ? 

8.  If  you  have  a  dozen  quart  cells,  how  can  you  make  them  equiva- 
lent to  one  3-gallori  cell  ? 

9.  If  a  battery  of  10  cells  have  an  E.M.F.  10  times  greater  than  that 
of  a  single  cell,  why  will  not  the  battery  yield  a  current  10  times  as 
strong  ? 

10.  (a)  The  internal  resistance  of  10  cells  connected  in  multiple  arc 
is  what  part  of  that  of  a  single  cell  ?     (b)  If  the  cells  were  connected  in 
series,  how  would  the  resistance  of  the  battery  compare  with  that  of  one 
of  its  cells  ?     (c)  How  would  the  E.M.F.  of  the  latter  battery  compare 
with  that  of  a  single  cell  ? 

11.  What  current  will  a  single  Bunsen  cell  furnish  against  an  external 
resistance  of  10  ohms  ? 

12.  What  current  will  8  Bunsen  cells,  in  series,  furnish  against  the 
same  resistance  ? 

77T  1      ft     V      ft 

SOLUTION  :        ^^  =  10+' (0.9X8)  =  °'83  +  amPere' 

13.  What  current  will  8  Bunsen  cells  in  multiple  arc  furnish  against 
the  same  external  resistance  ? 

E  1.8 


SOLUTION  : 


=  0.17  -f-  ampere. 


i  +  r       10  +  (0.9  -f  8) 

14.  What   current  will   a  Bunsen  cell   furnish   against  an  external 
resistance  of  0.4  ohm  ? 

15.  What  current  will   a  battery   of    two   Bunsen   cells,  in  series, 
furnish  against  the  same  resistance  as  the  last  ? 


312  ETHER    DYNAMICS. 

16.  What  current  will  2  cells  in  multiple  arc  furnish  against  the  same 
resistance  ? 

17.  A  coil  of  wire  having  a  resistance  of  10  ohms  carries  a  current  of 
1.5  amperes.     Required  the  difference  of  potential  at  its  ends. 

18.  (a)  The  resistance  between  two  points,  A  and  B,  of  a  conductor 
is  2.5  ohms ;  the  resistance  of  a  shunt  between  the  same  points  is  1.5 
ohms.     What  is  the  joint  resistance  between  these  points  ?     (6)  If  a  cur- 
rent of  10  amperes  be  maintained  between  these  points,  what  will  be  the 
strength  of  current  in  each  branch  ?     (c)  How  will  the  strength  of  cur- 
rent between  these  points  be  affected  if  the  shunt  be  removed  and  the 
same  fall  of  potential  be  preserved  ?     Why  ? 

19.  Three  conductors  have  conductances  of  4,  8,  10  mhos  ;  if  they  be 
joined  in  multiple  arc,  what  will  be  the  conductance  of  the  combination  ? 

20.  The  resistances  offered  by  three  conductors  are,  respectively,  2,  5, 
and  7  ohms.     What  will  be  their  joint  resistance  (a)  if  they  be  joined  in 
series  ?  (6)  if  they  be  joined  in  multiple  ? 

21.  Assume  that  the  electrical  dimensions  of  a  Daniell's  cell  are  as 
follows  :  E.  M.  F.  =  I  volt  and  r  =  2  ohms.     Let  a  complex  battery  be 
formed  of  10  Daniell's  cells  arranged  in  two  groups,  each  group  consist- 
ing of  5  cells  connected  in  series,  the  two  groups  being  connected  in 
multiple.     What  current '  will  the  battery  furnish  against  an  external 
resistance  of  3  ohms  ?    Ans.  f  ampere. 

22.  Suggest  some  device  by  means  of  which  the  strength  of  a  current 
flowing  through  any  instrument,  e.g.  a  motor  on  an  electric  car,  may  be 
easily  and  conveniently  changed  at  will. 

23.  The  E.  M.  F.  of  a  Grenet  cell  —  2  volts  ;  of  a  Daniell  cell  =  1  volt, 
(a)  On  what  condition  will  the  former  yield  a  current  twice  as  great  as 
the  latter  against  the  same  external  resistance  ?     (6)  How  may  this  con- 
dition be  attained  ? 

24.  How  many  cells  whose  dimensions  are  E.  M.  F.  =  1.8  volts  and 
r  =  1.1  ohms  will  be  required  in  series  to  send  a  current  of  .5  ampere 
against  an  external  resistance  of  50  ohms  ? 

25.  What  E.  M.  F.  is  required  to  maintain  a  current  of  .75  ampere  in 
a  lamp  whose  resistance  is  80  ohms  ? 

26.  If  a  circuit  have  a  large  resistance,  which  would  give  the  larger 
deflection,   a  high-resistance  or  a    low-resistance    coil    galvanometer? 
Why? 

27.  If  a  circuit  have  a  large  resistance,  should  the  helix  of  electro- 
magnets included  in  the  circuit  be  wound  with  short  large  wire,  or  with 
long  small  wire  ? 

28.  What  should  be  the  resistance  of  a  shunt,  that  a  galvanometer 
may  measure  j^  of  the  total  current  ? 


LAW   OF    MAGNETS.  313 

SECTION   VIII. 
MAGNETS    AND   MAGNETISM. 

337.  Law  of  Magnets.     Suspend  by  fine  threads  in  a  hori- 
zontal position  two  stout  darning  needles  which  have  been 
drawn  in  the  same  direction  (e.g.  from  eye  to  point)  several 
times   over   the   same   pole   of    a   powerful   electro-magnet. 
These  needles,  separated  a  few  feet  from  each  other,  take 
positions  parallel  with  each  other,  and  both  lie  in  a  northerly 
and  southerly  direction  with  the  points  of  each  turned  in  the 
same  direction. 

That  point  in  the  Arctic  zone  of  the  earth  toward  which 
magnetic  needles  point  is  called  the  north  magnetic  p6%  of 
the  earth.  That  end  of  the  needle  which  points  toward  the 
north  magnetic  pole  of  the  earth  is  called  the  north-seeking, 
marked,  or  +  pole  ;  this  is  the  end  that  is  always  marked  for 
the  purpose  of  distinguishing  one  from  the  other.  That  end 
of  the  needle  which  points  southward  is  called  the  south-seek- 
ing, unmarked,  or  —pole. 

Experiment  1.  Bring  both  points  near  each  other ;  there  is  a  mutual 
repulsion.  Bring  both  eyes  near  each  other  ;  there  is  a  mutual  repul- 
sion. Bring  a  point  and  an  eye  near  each  other ;  there  is  a  mutual 
attraction. 

Like  poles  of  magnets  repel,  unlike  poles  attract  each  other. 

338.  Magnetic  Transparency  and  Induction. 
Experiment  2.     Interpose  a  piece  of  glass,  paper,  or  wood-shaving 

between  the  two  magnets.  These  substances  are  not  themselves  percep- 
tibly affected  by  the  magnets,  nor  do  they  in  the  least  affect  the  attrac- 
tion or  repulsion  between  the  two  magnets. 

Substances  that  are  not  susceptible  to  magnetism  are  said 
to  be  magnetically  transparent.  When  a  magnet  causes 
another  body,  in  contact  with  it  or  in  its  neighborhood,  to 
become  a  magnet,  it  is  said  to  induce  magnetism  in  that 


314  ETHEB   DYNAMICS. 

body.     As  attraction,  and  never  repulsion,  occurs  between  a 
magnet  and  an  unmagnetized  piece  of  iron  or  steel,  it  must 


FIG.  253. 

be  that  the  magnetism  induced  in  the  latter  is  such  that 
opposite  poles  are  adjacent ;  that  is,  an  N  or  +  pole  induces  an 
S  or  —  pole  next  itself,  as  shown  in  Fig.  253. 

339.  Polarity. 

Experiment  3.  Strew  iron  filings  on  a  flat  surface,  and  lay  a  bar  mag- 
net on  them.  On  raising  the  magnet  it  is  found  that  large  tufts  of  filings 
cling  to  the  poles,  as  in  Fig.  254,  especially  to  the  edges  ;  but  the  tufts 

diminish  regularly  in  size  from  each  pole  towards  the  center, 

where  none  are  found. 

Magnetic  attraction  is  greatest  at  the  poles,  and  dimin- 
ishes towards  the  center,  where  it  is  nothing ;  i.e.  the 
center  of  the  bar  is  neutral.  This  dual  character  of 
the  magnet,  as  exhibited  at  its  opposite  extremities, 
is  called  polarity.  If  a  magnet  be  broken,  each  piece 
becomes  a  magnet  with  two  poles  and  a  neutral  line 
of  its  own. 

340.  Retentivity  and  Resistance. 

FIG.  254.  ft  is  more  difficult  to  magnetize  steel  than  iron  ;  on 
the  other  hand,  it  is  difficult  to  demagnetize  steel,  while  soft 
iron  loses  nearly  all  its  magnetism  as  soon  as  it  is  removed 
from  the  influence  of  the  inducing  body.  That  property  of 
steel  in  virtue  of  which  it  resists  the  escape  of  magne- 
tism which  it  has  once  acquired  is  called  retentivity.  The 
greater  the  retentivity  of  a  magnetizable  body,  the  greater  is 
the  resistance  which  it  offers  to  becoming  magnetized.  The 
harder  steel  is,  the  greater  is  its  retentivity.  Hence,  highly 
tempered  steel  is  used  for  permanent  magnets.  Hardened 


LINES    OF   MAGNETIC   FORCE. 


315 


iron  possesses  considerable  retentivity  ;  hence,  the  cores 
of  electro-magnets  should  be  made  of  the  softest  iron,  that 
they  may  acquire  and  part  with  magnetism  instantaneously. 

341.  Forms  of  Artificial  Magnets.  Artificial  magnets,  includ- 
ing permanent  magnets  and  electro-magnets,  are  usually  made  in  the 
shape  either  of  a  straight  bar  or  of  the  letter  U,  according  to  the  use  to  be 
made  of  them.  If  we  wish,  as  in  the  experiments  already  described,  to 
use  but  a  single  pole,  it  is  desirable  to  have  the  other  as  far  away  as  pos- 
sible ;  then,  obviously,  the  bar  magnet  is  more  convenient.  But  if  the 
magnet  is  to  be  used  for  lifting  or  holding  weights,  the  U-form  (see  Fig. 
258)  is  far  better,  because  the  attraction  of  both  poles  is  conveniently 
available. 

SECTION  IX. 
LINES    OF    MAGNETIC     FORCE.      THE    MAGNETIC    CIRCUIT. 


342.  Lines  of  Magnetic  Force. 

studied  by  the  use  of  iron  filings. 


These    lines    are    easily 
The  field  of  force  around 


FIG.  255. 


a  magnet  is  shown  by  placing  a  paper  over  it,  dusting  filings 
upon  the  paper,  and  tapping  it.     The  filings  take  symmetrical 


316 


ETHER    DYNAMICS. 


positions,  form  curves  between  the  poles  of  the  magnet  or 
magnets,  and  show  that  the  lines  of  force  connect  the  opposite 
poles  of  the  magnet.  The  fact  is  that  each  filing,  when 


PIG.  256. 

brought  within  the  influence  of  the  magnetic  field,1  becomes 
a  magnet  by  induction,  and  of  necessity  tends  to  take  a  defi- 
nite position  which  represents  the  resultant  of  the  forces 


XII  I /  ^_  l  '  ' 

\  x'  »    1   \  1  /  s       ~^-  \  \  '»     \  '   /  /  / 

\\\^  \  \ !  ///'^:::^<^\  \  I  /  r/y/ 


FIG.  257. 

acting  upon  it  from  each  pole  of  the  system.  ^4  Zme  of 
magnetic  force  is  a  line  drawn  in  such  a  manner  that  the 
tangent  to  it  at  any  point  indicates  the  direction  of  the 
resultant  magnetic  force  at  that  point  ;  or  it  is  a  line  at  every 

1  Surrounding  every  magnet  there  is  a  region  of  magnetic  influence,  technically 
known  as  the  magnetic  field. 


MAGNETIC   CIRCUIT. 


317 


point  of  which  the  axis  l  of  a  magnetic  needle  is  tangent. 
Fig.  255  represents  a  magnetic  field  photographed  from 
a  specimen  paper,  and  Fig.  256  is  a  graphical  representa- 
tion of  the  same.  In  this  illustration  the  unlike  poles  of 
two  magnets  are  placed  opposite  each  other.  Fig.  257  is 
a  diagram  of  paths  of  lines  of  force  of  a  bar  magnet  when 
its  axis  coincides  with  the  magnetic  meridian  of  the  earth 
(§  248)  and  its  N-pole  points  north; 
and  Fig.  258,  of  those  of  a  U-shaped 
magnet.  A  magnetic  pole  is  a  region 
within  a  magnet  towards  which  the 
lines  of  force  converge  or  from  which 
they  diverge. 


FIG.  258. 


343,  Magnetic  Circuit.  The  field 
of  a  magnet  is  permeated  with  lines  'r^ 
of  force,  which  may  be  more  con-  /  , 
veniently  called  magnetic  flux  paths,  '  { 
or  lines  of  flow.  A  line  of  force  is 
assumed  arbitrarily  to  start  from  the 
N-pole  and  to  pass  through  the  sur- 
rounding medium  (e.g.  the  air),  entering  the  magnet  by  the 
S-pole,  and  completing  its  path  through  the  magnet  itself  to 
its  starting  point  (the  N-pole),  thus  forming  a  complete  circuit 
(Fig.  257).  These  lines  do  not  all  emerge,  however,  from  the 
extremities.  A  multitude  of  lines  start  from  all  parts  of  the 
magnet  and  enter  at  corresponding  points  on  the  other  side 
of  its  central  or  neutral  line.  Every  line  of  magnetic  force 
makes  a  complete  circuit. 

The  exact  nature  of  magnetic  flux  is  not  understood,  but  it  appears  to 
be  attended  by  a  strain  in  the  ether.  It  possesses  several  peculiar  char- 
acteristics. 

In  air  and  most  other  mediums  the  lines  of  force  tend  to  separate  from 
one  another,  but  at  the  same  time  tend  to  become  as  short  as  possible. 

1  The  axis  of  a  needle  is  a  straight  line  connecting  its  poles. 


318  ETHER    DYNAMICS. 

The  strain  is  as  if  these  lines  were  stretched  elastic  threads  endowed  with 
the  property  of  repelling  one  another  as  well  as  of  shortening  them- 
selves ;  in  other  words,  there  is  tension  along  the  lines  and  repulsion  at 
right  angles  to  them.  They  may  be  likened  to  the  fibers  of  a  muscle 
which  contracts  and  at  the  same  time  thickens  when  exerting  force. 

If  the  N-pole  of  one  magnet  be  placed  opposite  the  S-pole  of  another 
(Fig.  256),  the  lines  of  force  issuing  from  the  former  enter  the  latter,  and, 
tending  to  shorten,  produce  attraction.  If  the  similar  ends  be  opposed 


FIG.  259. 

Fig.  259),  the  lines  of  force  are  turned  away  from  each  pole  in  all  direc- 
tions, and  complete  their  circuits  independently.  Thus  becoming  parallel, 
they  repel  one  another  ;  thus,  like  magnetic  poles  repel  each  other. 

It  would  seem  that  air  is  a  poor  conductor  of  lines  of  force,  or,  to  use 
a  technical  term,  its  permeability  is  low  ;  on  the  other  hand,  iron  is  highly 
permeable  to  lines  of  force.  If  a  piece  of  iron  be  brought  within  a  mag- 
netic field,  many  lines  of  force  will  leave  their  normal  paths  through  the 
air  and  crowd  together  in  this  medium  of  greater  permeability. 

Magnetic  flux  produces  the  following  important  effects  : 
(1)  A  bar  of  iron,  when  introduced  into  the  flux,  becomes 
magnetized.  (2)  A  freely  suspended  magnetic  needle  brought 
into  the  flux  comes  to  rest  in  a  definite  position.  (3)  An 
E.  M.  F.  is  developed  in  an  electric  conductor  when  it  is 
moved  across  the  flux  paths.1 

It  may  not  be  amiss  to  state  in  this  connection  that,  as 
a  result  of  comparatively  recent  experimental  and  mathe- 

1  It  is  possible  that  all  electric,  magnetic,  and  electro-magnetic  phenomena  are 
referable  to  two  conditions  of  stress  in  the  ether,  one  of  which  is  electric  flux  and 
the  other  magnetic  flux.  So  intimately  are  the  electric  and  magnetic  fluxes  corre- 
lated that  any  disturbance  in  one  immediately  calls  the  other  into  existence. 


THE   EARTH   A   MAGNET.  319 

matical  researches,  scientists  are  becoming  convinced  that 
electric  currents  are  transmitted  as  electric  waves  through 
the  ether  surrounding  a  conductor,  being  guided  by  the  con- 
ductor, but  not  transmitted  through  it. 

344.  Law  of  Inverse  Squares.     It  may  be  demonstrated 
experimentally  1  that  the  force  exerted  between  two  magnetic 
poles  varies  inversely  as   the  square  of  the  distance  between 
them. 

SECTION   X. 
TERRESTRIAL  MAGNETISM. 

345.  The  Earth  a  Magnet. 

Experiment.  Place  a  dipping  needle  2  over  the  +  pole  of  a  bar  mag- 
net (Fig.  260).  The  needle  takes  a  vertical  position  with  its  —  pole  down. 
Slide  the  supporting  stand 
along  the  bar ;  the  —  pole 
gradually  rises  until  the 
stand  reaches  the  middle 
of  the  bar,  where  the 
needle  becomes  horizon- 
tal. Continue  moving  the 

stand  toward  the  —  pole  of  the  bar  ;  after  passing  the  middle  of  the  bar 
the  +  pole  begins  to  dip,  and  the  dip  increases  until  the  needle  reaches 
the  end  of  the  bar,  when  the  needle  is  again  vertical  with  its  +  pole 
down. 

If  the  same  needle  be  carried  northward  or  southward  along  the 
earth's  surface,  it  will  dip  in  the  same  way  as  it  approaches  the  polar 
regions,  and  be  horizontal  only  at  or  near  the  equator. 

The  experiment  presents  within  a  small  compass  a  series  of 
phenomena  precisely  similar  to  those  caused  by  the  earth's 
influence  upon  the  dipping  needle,  and  this  leads  to  the  con- 
clusion that  the  earth  is  a  magnet.  In  other  words,  these  phe- 
nomena .are  just  what  we  should  expect  if  a  huge  magnet 

1  See  the  author's  "  Principles  of  Physics,"  p.  528. 

2  A  magnetic  needle  supported  on  a  horizontal  axle  so  that  it  can  rotate  in  a 
vertical  plane  is  called  a  dipping  needle. 


320 


ETHER   DYNAMICS. 


were  thrust  through  the  earth,  as  represented  in  Fig.  261  — 
having  its  N-pole  near  the  S  geographical  pole,  and  its  S-pole 
near  the  N  geographical  pole ; l  or  if  the  earth  itself  were 
a  magnet. 


FIG.  261. 

346.  Magnetic  Poles  of  the  Earth.  Places  where  the  dip* 
ping  needle  assumes  a  vertical  position  are  called  the  mag- 
netic poles  of  the  earth.  A  point  was  found  on  the  western 
coast  of  Boothia  by  Sir  James  Ross,  in  the  year  1831,  where 
the  dipping  needle  lacked  only  one  sixtieth  of  a  degree  of 
pointing  directly  to  the  earth's  center.  The  same  voyager 
subsequently  reached  a  point  in  Victoria  Land  where  the 
opposite  pole  of  the  needle  lacked  only  1°  20'  of  pointing  to 
the  earth's  center. 

1  In  common  parlance  the  magnetic  poles  of  the  earth  are  positions  on  the  earth's 
surface  where  a  dipping  needle  points  vertically  downward.  The  direction  in  which 
such  a  needle  points  would  meet  the  direction  in  which,  for  example,  a  needle  at 
Boston  points,  at  some  thousand  miles  down  in  the  bowels  of  the  earth,  which  shows 
that  the  poles  or  centers  of  magnetic  action  are  really  deep-seated  ;  hence,  the  phrase 
magnetic  poles  on  the  earth's  surface  is  somewhat  misleading. 


VARIATION    OF    THE 


It  will  be  seen  that,  if  we  call  that  end  of  a  magnetic  needle  which 
points  north  the  N-pole,  we  must  call  that  magnetic  pole  of  the  earth 
which  is  in  the  northern  hemisphere  the  S-pole.  (See  Fig.  261.)  To 
avoid  confusion,  many  careful  writers  abstain  from  the  use  of  the  terms 
north  and  south  poles,  and  substitute  for  them  the  terms  positive  and  neg- 
ative, or  marked  and  unmarked  poles. 

347.  Variation  of  the  Needle,     Inasmuch  as  the  magnetic 
poles  of   the  earth  do  not  coincide   with   the    geographical 
poles,  it  follows  that  in  most  places  the  needle  does  not 
point  due  north  and  south.     The  angle  which  the  vertical 
plane  through  the  axis  of  a  freely  suspended  needle  makes 
with  the  geographical  meridian  of  the  place  is  known  as  the 
angle  of  declination.     In  other  words,  the  angle  of  declination 
is  the  angle  formed  by  the  magnetic  and  the  geographical 
meridians.     This  angle  differs  at  different  places. 

348.  Isogonic  Curves.     These  are  lines   connecting  all  points  of 
equal  declination  on  the  earth's  surface.     The  line  of  no  declination,  or 
isogonic  of  0°  (Fig.  262),  commences  at  the  N  magnetic  pole  about  lat. 


FIG.  262. 


70°,  long.  96°,  passes  in  a  southeasterly  direction  across  Lake  Erie  and 
Western  Pennsylvania,  and  enters  the  Atlantic  Ocean  near  the  boundary 
between  the  Carolinas.  Pursuing  its  course  through  the  south  polar 


322 


ETHER    DYNAMICS. 


regions,  it  reappears  in  the  eastern  hemisphere  and  crosses  Western  Aus- 
tralia and  the  Caspian  Sea,  and  thence  passes  to  the  Arctic  Ocean. 
There  is  also  a  detached  line  of  no  declination  enclosing  an  oval  area  in 
Eastern  Asia  and  the  Pacific  Ocean.  In  all  the  New  England  states  and 
in  the  states  of  Pennsylvania  and  New  York  the  declination  is  westward. 
In  all  the  states  west  of  these  states  the  declination  is  eastward. 

The  magnetic  poles  are  not  fixed  objects  that  can  be  located  like  an 
island  or  cape,  but  are  constantly  changing.  They  appear  to  swing, 
something  like  a  pendulum,  in  an  easterly  and  westerly  direction,  each 
swing  requiring  centuries  to  complete  it.  The  north  magnetic  pole  is 
now  on  its  westerly  swing,  and  consequently  the  line  of  no  declination 
is  slowly  moving  westward. 


SECTION   XI. 

MAGNETIC    RELATIONS    OF   THE   CURRENT. 
MAGNETS. 


ELECTRO- 


349.  Magnetic  Field  due  to  a  Circular  Current.  If  a  wire 
be  bent  into  the  form  of  a  circle  of  about  10  in.  diameter, 
and  placed  vertically  in  the  magnetic  meridian,  and  a  card- 
board be  placed  at  right  angles  to  the  circle  so  that  its  hori- 


FIG.  263. 


zontal  diameter  is  coincident  with  the  upper  surface  of  the 
cardboard,  and  a  very  strong  current  be  sent  through  the  wire 
in  the  direction  indicated  by  the  arrowhead  in  the  wire,  iron 


SOLENOID.  323 

filings  sifted  upon  the  card  will  arrange  themselves  as  shown 
in  Fig.  263.  And  if  a  small  compass  be  carried  inside  and 
outside  the  circle,  the  several  positions  taken  by  the  needle, 
as  indicated  in  the  figure  by  arrows,  corroborate  the  directions 
of  the  lines  of  force  as  indicated  by  the  filings.  If  the  direc- 
tion of  the  current  be  reversed,  the  direction  of  the  needle 
will  be  reversed  wherever  it  may  be  placed.  The  electric 
current  and  its  encircling  lines  of  force  *  always  coexist,2  and 
one  varies  directly  as  the  other ;  that  is,  the  greater  the 
strength  of  the  current,  the  greater  is  the  number  of  lines  of 
force  that  occupy  the  field. 

350,  Solenoid.     If  instead  of  a  single  circle  of   wire  an 
insulated  wire  be  wound  into  a  helix  of  several  turns,  it  is 
called  a  solenoid.     The  in- 
tensity  of   the    magnetic 
field  is  greatly  increased 
by  the  joint  action  of  the 
many  current  turns.     The 
passage  of  an  electric  cur- 
rent  through   a  solenoid 

FIG. 264. 

gives  it  all  the  properties 

of  a  magnet.     To  within  a  short  distance  of  its  ends  the  lines 

of  force  are  parallel  with  its  axis,  as  shown  in  Fig.  264. 

A  solenoid  encircling  an  iron  core  constitutes  an  electro- 
magnet. By  reason  of  its  permeability  the  iron  core  greatly 
increases  the  number  of  lines  of  force  which  pass  through 
the  solenoid.  Hence,  the  magnetic  strength  of  a  solenoid  is 
greatly  increased  by  the  presence  of  an  iron  core. 

1  "  Every  conducting  wire  is  surrounded  by  a  sort  of  magnetic  whirl.  A  great  part 
of  the  energy  of  the  so-called  electric  current  in  the  wire  consists  in  these  external 
magnetic  whirls.     To  set  them  up  requires  an  expenditure  of  energy  ;  and  to  main- 
tain them  requires  a  constant  expenditure  of  energy.     It  is  these  magnetic  whirls 
which  act  on  magnets,  and  cause  them  to  set,  as  galvanometer  needles  do,  at  right 
angles  to  the  conducting  wire."  —  S.  P.  THOMPSON. 

2  "  Electricity  in  motion  produces  magnetic  force,  and  magnetism  in  motion  pro- 
duces electric  force."  —  HERTZ. 


324 


ETHE&   DYNAMICS. 


351,  Polarity  of  an  Electro-magnetic  Solenoid. 

Experiment.     Fig.  265  represents   a  small   cell   floating  on  water. 

The  leading  out  wire  of  the  cell  is  wound  into  a  horizontal  solenoid. 

Slowly,  after  the  cell  is 
floated,  it  will  take  a  posi- 
tion so  that  the  axis  of 
the  solenoid  will  point 
north  and  south  like  a 
magnetic  needle.  Hold 
the  S-pole  of  a  bar  magnet 
near  that  end  of  the  solen- 
oid which  points  north; 
FIG.  265.  the  solenoid  is  attracted 

by  the  magnet.     Hold  the  N-pole  of  the  magnet  near  the  north-pointing 

end  of  the  solenoid  ;  the  magnet  repels  the  solenoid. 
Repeat  the  above,  using  in  place  of 

the  bar  magnet  another  current-bear- 

ing  solenoid  (Fig.  266)  ;  there  will  be 

a  repetition  of  the  phenomena  obtained 

with  the  bar  magnet. 

Place  the  wire  of  another  battery 

over  and  parallel  with  the  coil  (Fig. 

267),  so  that  the  two  currents  will  flow 

in  planes  at  right  angles  to  each  other. 

The  coif  is  deflected  like  a  magnetic  needle  (Fig.  268).     Reverse  the 

direction  of  the  current  above  and  the  deflection  is  reversed. 


FIG.  2G6. 


FIG.  267. 


FIG. 268. 


We  thus  prove  that  a  solenoid  bearing  a  current  possesses 
polarity  as  if  it  were  a  magnet,  and  that  there  can  be  pro- 
duced by  a  current-bearing  solenoid  a  magnetic  field  of  the 
same  character  as  that  produced  by  a  permanent  magnet. 


KULES    TO    FIND    POLES    OF    THE    SOLENOID. 


325 


There  is  no  essential  difference  between  a  permanent  mag- 
net, a  current-bearing  solenoid,  and  an  electro-magnet,  except 
that  the  last  may  be  made  much  stronger  than  either  of  the 
others. 

352,  Given  the  Direction  of  the  Current  in  a  Solenoid,  to 
Find  the  N-  and  S-poles  of  the  Solenoid,  and  vice  versa. 

RULE  1.  Place  the  palm  of  the  right  hand  against  the 
side  of  the  solenoid  so  that  the  fingers  will  point  in  the  direc- 
tion of  the  current  passing  through  the  windings  (as  shown  in 
Eig.  269)  ;  the  thumb 
will  point  in  the  direc- 
tion of  the  \\-pole  of 
the  solenoid  or  electro- 
magnet.1 


FIG.  269. 


RULE  2.  Ascertain 
the  N-pole  of  the  solen- 
oid or  electro-magnet 
withamagnetic  needle, 
and  place  the  palm  of 
the  right  hand  upon 

the  solenoid  so  that  the  outstretched  thumb  points  in  the  direction 
of  the  N-pole  ;  the  fingers  will  point  in  the  direction  in  which 
the  current  passes  in  the  windings. 

Fig.  270  represents  the  two  poles  of  a  U-shaped  electro-magnet,  and 
shows  the  method  in  which  the  wire  is  wound  in 
the  two  helices  and  the  relative  direction  of  the 
current  in  the  same.  It  will  be  seen  that  that 
is  the  S-pole  about  which  the  current  flows  in  the 
direction  in  which  the  hands  of  a  clock  move, 
FIG.  270.  while  that  is  the  N-pole  about  which  the  current 

has  an  anti-clockwise  motion.  Evidently,  if  the  current  be  reversed  the 
polarity  will  be  reversed. 

1  The  following  suggestion  will  often  prove  of  practical  value  :  that  is  the  south 
pole  of  a  helix  where  the  current  corresponds  to  the  motion  of  the  hands  of^a  watch, 
Sj^and  that  is  the  north  pole  where  the  current  is  in  the  reverse  direction,  N. 


326 


ETHER    DYNAMICS. 


SECTION  XII. 
ELECTRODYNAMICS.      AMPERE'S  THEORY    OF    MAGNETISM. 

353.  Mutual  Action  of  Currents  on  One  Another,     If  we 
suppose  that  a  test-needle  be  moved  up  or  down  just  back  of 


I  t 


t  I 


A  B 

FIG.  271. 


FIG.  273. 


ATT 
/  •  \ 


the  current-bearing  wires   (Fig.  271),  the  N- 
•      and  S-poles  will  take  the  positions  indicated 
by  n  and  s.     From  inspection  of  the  polarity 
REPULSION          developed,  we  may  readily  predict  that  if  the 
/•V       /•)  wires  were  so  suspended  as  to  be  free  to  move 
^-^   either  toward  or  from  each  other,  the  pair  of 

FIG.  272. 

wires  in  which  the  currents  flow  parallel  to 

each  other  and  in  the  same  direction,  A,  would  attract  each 
other,  and  the  pair  of  wires  in  which  the  currents  flow  in 
opposite  directions,  B,  would  repel  each  other  ;  l  but  if  the 
currents  be  inclined  to  each  other,  as  in  Fig.  273,  they  will 
tend  to  move  into  a  position  in  which  they  will  be  parallel 
and  in  the  same  direction.  That  this  actually  takes  place 
may  be  shown  by  the  following  experiments  : 


1  Fig.  272  shows  the  cross  section  of  the  wires  in  the  two  cases  and  the  direc- 
tions of  the  lines  of  force  encircling  the  wires.    Compare  with  Fig.  258. 


AMPERE'S  LAWS. 


327 


Experiment  1.  Fig.  274  represents  a  portion  of  a  divided  circuit. 
The  lower  ends  of  the  wires  dip  into  mercury  about  one  sixteenth  of  an 
inch,  and  the  wires  are  so  suspended  that  they  are  free  to  move  toward 
or  from  each  other.  Send  the  current  of  a  battery  of  three  or  four  Bun- 
sen  cells,  in  multiple  arc,  through  this  divided  circuit.  The  two  portions 
of  the  current  travel  in  the  same  direction  and  parallel  with  each  other, 
and  the  two  wires  at  the  lower  extremities  move 
toward  each  other,  showing  an  attraction. 

Experiment  2.  Make  the  connections  (Fig.  275) 
so  that  the  current  will  go  down  one  wire  and  up 
the  other.  They  repel  each  other. 

In  the  experiment  with  the  floating  cell 
and  current-bearing  wire  placed  over  and 
parallel  to  the  solenoid  (Fig.  267),  a  care-  FlG- 274-  FlG- 275- 
fill  examination  will  disclose  the  fact  not  only  that  the 
planes  in  which  the  current  flows  in  the  coil  tend  to  become 
parallel  to  the  current  above,  but  that  the  current  in  the 
upper  half  of  the  coil,  where  the  influence  due  to  proximity 
is  greatest,  tends  to  place  itself  so  as  to  flow  in  the  same 
direction  as  that  of  the  current  above. 

354.  Ampere's  Laws.      LAW    1.     Parallel   currents   in   the 
same  direction  attract  one  another  ;  parallel  currents  in  oppo- 
site directions  repel  one  another. 

LAW  2.     Currents  that  are  not  parallel  tend  to  become  par- 
allel and  flow  in  the  same  direction. 

355.  Ampere's  Theory  of  Magnetism.    This  celebrated  the- 
ory, briefly  stated,  is  that  magnets  and  solenoid  systems  are 
fundamentally  the  same;  that  magnetism  is  simply  electricity 
in  rotation,  and  that  a  magnetic  field  is  a  sort  of  whirlpool  of 
electricity.     Not,  of  course,  that  a  steel  magnet  contains  an 
electric  current  circulating  round  and  round  it,  as  does  an 
electro-magnet,  but  that  every  molecule  of  iron,  steel,  or  other 
magnetizable  substance,  is  the  seat  of  a  separate  current  cir- 
culating round  it  continuously  and  without  resistance,  and 
thus  that  every  molecule  is  a  magnet. 


328  ETHER    DYNAMICS. 

According  to  this  theory,  in  an  unmagnetized  bar  these  currents  lie  in 
all  possible  planes,  and,  having  no  unity  of  direction,  they  neutralize  one 
another,  and  so  their  effect  as  a  system  is  zero.  But  if  a  current  of  elec- 
tricity or  a  magnet  be  brought  near,  the  effect  of  the  induction  is  to  turn 
the  currents  into  parallel  planes,  and  in  the  same  direction,  in  conformity 
to  Ampere's  Second  Law.  If  the  retentivity  be  strong  enough,  this 
parallelism  will  be  maintained  after  the  removal  of  the  inducing  cause, 
and  a  permanent  magnet  is  the  result. 


FIG.  276. 

Intensity  of  magnetization  depends  on  the  degree  of  parallelism,  and 
the  latter  depends  on  the  strength  of  the  influencing  magnet.  When 
these  currents  have  become  quite  parallel,  the  body  has  received  all  the 
magnetism  that  it  is  capable  of  receiving,  and  is  said  to  be  saturated. 

The  hypothetical  currents  that  circulate  round-  a  magnetic  molecule 
we  shall  call  amperian  currents,  to  distinguish  them  from  the  known  cur- 
rent that  traverses  the  solenoid.  In  strict  accordance  with  this  theory, 
the  poles  of  the  electro-magnet  are  determined  by  the  direction  of  the 
current  *in  the  helix.  The  inductive  influence  of  the  electric  current 
causes  the  amperian  currents  to  take  the  same  direction  with  itself,  as 
represented  in  Fig.  276. 

SECTION   XIII. 
ELECTRO-MAGNETIC   INDUCTION. 

356.  Description  of  Apparatus.  A  (Fig.  277)  is  a  "  short 
coil"  of  coarse  wire  (i.e.  the  wire  which  it  contains  is  com- 
paratively short),  and  has,  of  course,  little  resistance.  B  is  a 
"  long  coil "  of  fine  wire  having  many  turns.  Coil  A  is  in 
circuit  with  a  voltaic  cell.  This  circuit  we  call  the  primary 
circuit,  the  current  in  this  circuit  the  primary  or  inducing 
current,  and  the  coil  the  primary  coil.  Another  circuit,  hav- 
ing in  it  no  cell  or  other  means  of  generating  a  current, 


ELECTROMAGNETIC    INDUCTION. 


329 


FIG.  277. 


contains  coil  B  and  a  galvanoscope  with  an  astatic  needle.1 
This  circuit  is  called  the  secondary  circuit,  the  coil  the  second- 
ary coil,  and  the  currents  which  cir- 
culate through  this  circuit  are  called 
secondary  or  induced  currents. 

Experiment  1.  Lower  the  primary 
coil  quickly  into  the  secondary  coil,  watch- 
ing at  the  same  time  the  needle  of  the  gal- 
vanoscope to  see  whether  it  moves,  and, 
if  so,  in  what  direction.  Simultaneously 
with  this  movement  there  is  a  movement 
of  the  needle,  showing  that  a  current  must 
have  passed  through  the  secondary  circuit. 
Let  the  primary  coil  rest  within  the  sec- 
ondary until  the  needle  comes  to  rest. 

After  a  few  vibrations  the  needle  settles  at  zero,  showing  that  the 
secondary  current  was  a  temporary  one.  Now,  watching  the  needle, 
quickly  pull  the  primary  coil  out ;  another  deflection  in  the  opposite 
direction  occurs,  showing  that  a  current  in  the  opposite  direction  is 
caused  by  withdrawing  the  coil. 

It  is  evident  that  in  this  case  the  current  does  not  by  its 
mere  presence  cause  an  induced  current,  but  that  a  change  in 
the  relative  positions  of  the  two  circuits,  one  of  which  bears 

a    current,  is   neces- 
sary. 

Instead  of  a  cur- 
rent-bearing coil  a 
bar  magnet  may  be 
introduced  into  the 
secondary  coil, and  af- 
terwards withdrawn 
from  it.  The  needle  is  deflected  at  each  act,  as  before. 


FIG.  278. 


1  This  needle  consists  of  two  needles  of  about  the  same  intensity  with  their  poles 
reversed,  fixed  parallel  with  each  othe».  Though  the  needles  nearly  neutralize  each 
other,  and  are  therefore  little  affected  by  the  field  of  the  earth's  magnetism,  they  are 
especially  sensitive  to  the  influence  of  the  electric  current, 


330  ETHEK    DYNAMICS. 

Experiment  2.  Place  the  primary  coil  within  the  secondary.  Open 
the  primary  wire  at  some  point  and  then  close  the  circuit  (Fig.  278)  by 
bringing  into  contact  the  extremities  of  the  wires.  A  deflection  is  pro- 
duced. As  soon  as  the  needle  becomes  quiet,  break  the  circuit  by  sepa- 
rating the  wires ;  a  deflection  in  the  opposite  direction  occurs. 

The  same  phenomena  occur  when  the  primary  current  is 
by  any  means  suddenly  strengthened  or  weakened. 

An  examination  of  the  direction  of  these  currents  enables 

us  to  state  the  facts  as  fol- 

o,        ,. 

lows  :  Starting  a  current  in 
a  primary,  increasing  the 
strength  of  the  primary  cur- 
rent, or  moving  the  primary 
nearer  (Fig.  279)  produces 

in  the  secondary  a  transitory  current  in  the  opposite  direction. 
Stopping  the  primary,  diminishing  the  strength  of  the  pri- 
mary, or  moving  the  primary  away  (Fig.  279),  causes  in  the 
secondary  a  transitory  current  in  the  same  direction. 

It  is  evident,  therefore,  that  the  conditions  under  which 
a  current  in  the  primary  coil  can  cause  a  current  in  a  neigh- 
boring secondary  depend  upon  some  change  either  in  the 
strength  of  the  primary  current  or  in  the  relative  positions 
of  the  primary  and  secondary  circuits. 

The  act  by  which  the  primary,  or  a  magnet,  causes  a  cur- 
rent in  a  neighboring  secondary  is  called  magneto-electric 
induction. 

357.  Faraday's  Law  of  Induction.  If  any  conducting  cir- 
cuit be  placed  in  the  magnetic  field,  then,  if  a  change  of  rela- 
tive position  or  change  of  strength  of  the  primary  current 
cause  a  change  in  the  number  of  lines  of  force  passing  through 
the  secondary,  an  electro-motive  force  is  set  up  in  the  second- 
ary proportional  to  the  rate  at  which  the  number  of  lines  of 
force  included  by  the  secondary  is  varying. 


MICHAEL    FARADAY. 


INDUCTION. 


331 


Consider  the  case  of  induction  by  a  magnet.  Let  S  (Fig.  280)  be  a 
secondary  circuit  and  N  a  magnet  projecting  a  certain  number  of  lines 
of  force  through  the  circuit.  If  S  be  moved  nearer  to  the  magnet,  say  to 
S',  a  much  greater  number  of 
lines  of  force  of  the  magnet  pass 
through  the  circuit  than  when  in 
its  former  position,  owing  to  the 
divergence  of  the  lines  as  they 
recede  from  the  pole. 

358.  Earth  Induction.  Call 
to  mind  that  the  earth  itself  is  a 
great  magnet,  and  that  its  lines 
of  force  pass  through  our  atmos- 
phere from  pole  to  pole,  and  it 
will  be  easy  to  conceive  that  the  Fl° 

mere  motion  of  a  coil  of  wire  about  an  axis  properly  placed 1  is  all  that 
is  necessary  to  produce  a  current.     Such  a  coil  with  a  galvanometer,  G, 


FIG.  281. 

in  circuit  is  represented  in  Fig.  281.  The  rotation  of  the  coil  across  the 
magnetic  flux  encircling  the  earth  causes  the  coil  to  be  alternately  filled 
with  and  emptied  of  this  flux,  and  thereby  an  E.  M.  F.  is  generated  in 
the  coil,  and  this  causes  currents  to  flow  through  the  galvanometer. 

1  The  coil  should  be  placed  at  right  angles  to  the  direction  of  the  dip  at  the 
locality. 


332  ETHER   DYNAMICS. 

359.  Self-induction,     At  the  instant  that  a  current  enters  a 
circuit,  and  while  the  magnetic  flux  is  enveloping  a  conductor, 
an  E.M.F.  opposite  to  that  of  the  advancing  (or  inducing) 
current  is  developed,  thus  opposing  the  current  which  pro- 
duces it.     But  when  the  magnetic  flux  decreases  (e.g.  when 
the  circuit  is  broken)  an  E.M.F.  having  a  direction  the  same 
as  that  of  the  retiring  current  is  established.     This  action  is 
called  self-induction.     Thus  it  appears  that  when  the  current 
starts,  self-induction  prevents  it  from  rising  instantly  to  its 
full  strength  ;  when  the  current  stops,  self-induction  tends  to 
prolong  the  flow.    In  both  cases  the  effect  is  only  momentary. 

The  momentary  current  at  breaking  the  circuit  is  called 
the  extra  current.  This  current  has  a  high  E.M.F.,  and  is 
the  cause  of  the  spark  seen  whenever  a  strong  current  is 
interrupted.  If  the  circuit  contain  an  electro-magnet  the 
spark  is  much  intensified.  Between  every  pair  of  turns 
of  any  coil  there  is  a  mutual  inductance  which  is  a  part  of 
the  self-inductance  of  the  coil.  It  is  this  principle  that  is 
utilized  in  the  "  spark-coils "  employed  in  voltaic  circuits  for 
lighting  gas. 

360.  Induction  Coils.     If  a  core  of  iron,  or,  still  better, 
a  bundle  of  wires  (A  A,  Fig.  282),  be  inserted  in  the  primary 
coil,  it  is  evident  that  it  will  be  magnetized  and  demagnetized 
every  time  the  primary  is  made  and  broken.     The  starting 
and  cessation  of  amperian  currents  in  the  core  in  conjunc- 
tion with  the  commencement  and  ending  of  the  primary  cur- 
rent greatly  intensifies  the  secondary  currents.     To  save  the 
trouble  of  making  and  breaking  by  hand,  the  core  is   also 
utilized  in  the  construction  of  an  automatic  make-and-break 
piece.     A  soft  iron  hammer,   b,  is  connected  with  the  steel 
spring  c,  which  is  in  turn  connected  with  one  of  the  termi- 
nals of  the  primary  wire.     The  hammer  presses  against  the 
point  of  a  screw,  d,  and  thus,  through  the  screw,  closes  the 
circuit.     But  when  a  current  passes  through  the  primary  wire, 


KUHMKORFF  S    CELLS. 


333 


the  core  A  A  becomes  magnetized,  draws  the  hammer  away 
from  the  screw,  and  breaks  the  circuit.  The  circuit  broken, 
the  core  loses  its  magnetism,  and  the  hammer  springs  back 


FIG.  282. 

and  closes  the  circuit  again.  Thus  the  spring  and  hammer 
vibrate,  and  open  and  close  the  primary  circuit  with  great 
rapidity.  Such  an  instrument  is  called  an  induction  coil. 

361,  Ruhmkorff's  Coil.  This  instrument  has  the  important 
addition  to  the  parts  already  explained  of  a  condenser,  B  B 
(Fig.  282).  This  consists  of  two  sets  of  layers  of  tin  foil 
separated  by  paraffined  paper ;  the  layers  are  connected 
alternately  with  one  and  the  other  electrode  of  the  battery, 
as  the  figure  shows,  so  that  they  serve  as  a  sort  of  expansion 
of  the  primary  wire. 

The  effect  of  the  condenser  seems  to  be  to  prevent  spark- 
ing at  the  make-and-break  piece,  and  thereby  to  render  the 
interruption  of  the  primary  current  more  abrupt,  and  hence 
the  E.  M.  F.  of  the  secondary  is  much  increased. 


334  ETHER    DYNAMICS. 

Secondary  currents  developed  in  high  resistance  coils 
are,  as  we  ought  to  expect,  distinguished  from  primary,  or 
voltaic  currents,  by  their  vastly  greater  E.  M.  F.,  or  power  to 
overcome  resistances.  A  coil  constructed  for  Mr.  Spottis- 
woode,  of  London,  has  280  miles  of  wire  in  its  secondary  coil, 
and  0.7  mile  of  wire  in  the  primary.  With  five  voltaic  cells 
this  coil  gives  a  secondary  spark  forty-two  inches  long,  and 
can  perforate  glass  three  inches  thick.  Many  brilliant  experi- 
ments may  be  performed  with  these  coils. 

Experiment  3.  Connect  a  battery  of  two  Bunsen  cells,  in  multiple  arc, 
with  a  Ruhmkorff  coil  (Fig.  283).  Bring  the  electrodes  of  the  secondary 
coil  within  from  one  fourth  of  an  inch  to  one  inch  of  each  other,  accord- 

*n^  to  the  caPacitv  °f  tne  instrument. 
A  series  of  sparks  in  rapid  succession 
pass  from  pole  to  pole. 

Experiment  4.    Introduce  a  Geissler 
tube.  A,  into  the  secondary  circuit.   These 
tubes  .contain  highly  rarefied  gases  of 
ii    different    kinds.      Platinum    wires    are 
i    sealed  into  the  glass  at  each  end  to  con- 
duct the  electric  current  through  the 
glass.     The  sparks  become  diffused  in 
FIG.  283.  these  tubes  so  as  to  illuminate  the  entire 

tubes  with  an  almost  continuous  glow. 

Observe  that  the  electrodes  are  separated  from  each  other  much  more 
widely  than  would  be  admissible  in  air  of  ordinary  density,  showing 
that  rarefied  gases  offer  less  resistance  than  dense  gases.  Gases  have 
been  so  highly  rarefied,  however,  that  an  electric  current  would  not 


In  vacuum  tube  discharges  the  negative  electrode  can  be  distinguished 
from  the  positive  electrode  by  the  dark  space  which  surrounds  it,  and  by 
a  patch  of  deep  blue  light  which  intervenes. 

362.  The  Induction  Coil  Reversible.  An  induction  coil  is 
in  ascertain  sense  a  reversible  machine.  If  a  current  of 
considerable  strength  circulate  under  small  E.  M.  F.  in  the 
primary,  then  variations  in  its  strength  give  rise  to  very 
weak  currents  of  exceedingly  high  E.  M.  F.  in  the  secondary. 


THE    TRANSFORMER. 


335 


Conversely,  if  we  cause  to  circulate  in  the  secondary  weak 
currents  under  very  high  E.  M.  F.,  by  their  fluctuations  there 
will  be  generated  in  the  primary  strong  currents  of  small 
E.  M.  F.  We  do  not  in  either  case  create  electric  energy. 
Electric  power  is  the  product  of  two  factors,  current  and  elec- 
tro-motive force.  The  induction  coil  enables  us  to  increase 
one  of  these  factors  at  the  expense  of  the  other,  and  to 
transform  electric  energy  in  form  much  as  a  mechanical 
power  (e.g.  a  lever)  enables  us  to  convert  a  quantity  of  work 
which  consists  of  small  stress  exerted  through  a  great  dis- 
tance into  a  large  stress  exerted  through  a  small  distance. 

363.  The  Transformer.  The  transformer — sometimes  called 
a  converter  —  is  merely  an  induction  coil  used  to  change  the 
relation  of  the  number  of  volts  to  the  number  of  amperes  of 
any  current.  In  a  perfect  transformer  the  number  of  watts 
in  the  primary  equals  the  number  of  watts  in  the  secondary. 

The  Euhmkorff  coil  as  ordinarily  used  may  be  regarded 
as  a  "step  up"  transformer  from  low  potential  to  high 
potential.  But  if  the  coil  of  long  thin  wire  be  used  as  the 
primary,  it  becomes  a  "  step  down "  transformer  from  high 
potential  to  low  potential. 


FIG.  284. 


FIG.  285. 


Fig.  284  represents  the  coils  of  a  transformer  used  in  the  incan- 
descent lamp  service,  and  Fig.  285  represents  the  same  enclosed  in  a  case. 
The  transformer  is  applied  in  the  welding  of  metals,  i.e.  to  fuse  the 


336  ETHER 'DYNAMICS. 

ends  of  metals  that  are  to  be  joined  together,  where  many  hundred  or 
even  thousand  amperes  of  current,  and  only  a  fraction  of  a  volt,  would 
be  required  for  an  instant. 

A  still  wider  application  of  transformers  is  in  the  transmission  of 
electric  power.  The  power  of  a  current  equals  C2  R.  That  is,  when  the 
current  strength  is  doubled  there  will  be  four  times  as  much  energy 
transformed  per  second.  We  see,  then,  that  to  transfer  electric  energy 
to  a  great  distance  it  may  be  desirable  to  have  a  high  E.  M.  F.  with  a 
small  current  passing  through  the  mains,  and  then  to  reduce  the  E.  M.  F. 
and  increase  the  current  by  a  transformer  at  the  place  where  the  energy 
is  to  be  used.  By  this  means  the  expense  involved  in  the  copper  con- 
ductors is  much  reduced. 

For  electric  lighting  in  private  houses  transformers  are  used  to  bring 
down  the  high  potential  of  the  mains  to  the  safe  limit  of  about  100  volts. 
These  transformers  are  usually  supported  on  the  street  poles. 


SECTION  XIV. 
DYNAMO-ELECTRIC   MACHINES. 

364.  Principles  of  the  Dynamo.  The  dynamo  is  a  device 
for  transforming  mechanical  energy  into  electric  energy.  In 
the  most  improved  types  of  dynamos  this  is  done  with  a  loss 
of  less  than  five  per  cent  of  the  energy. 

The  action  of  the  dynamo  is  based  on  the  principle  of  cur- 
rent induction.  It  embraces  a  system  of  coils  which  revolve 
in  a  magnetic  field  in  such  a  way  that  the  number  of  lines  of 
force  passing  through  them  varies  continuously.  As  we  have 
previously  learned,  this  creates  a  difference  of  potential  in  the 
system,  so  that  if  the  points  of  different  potential  be  con- 
nected by  a  wire,  a  current  will  be  established  in  the  circuit. 

Experiment.  Connect  a  flat  coil  of  about  two  inches  in  diameter 
having  several  turns  of  wire,  with  a  delicate  galvanometer,  and  rotate 
the  coil  at  one  of  the  poles  of  a  strong  magnet  on  an  axis  at  right  angles 
to  the  axis  of  the  magnet  and  the  lines  of  force,  as  illustrated  in  Fig.  286. 

The  horizontal  arrow  a  indicates  the  direction  of  the  mag- 
netic lines  of  force,  the  horizontal  arrow  b  the  direction  of 
motion  of  the  end  of  the  coil  of  wire,  and  the  vertical  arrow  c 


PRINCIPLES    OF    THE    DYNAMO.  337 

the  direction  of  the  current  induced  in  the  coil  of  wire  from 
the  movement  of  the  coil  across  the  field  of  magnetic  force  in 
such  a  manner  that  the  number  of  lines  of  force  threading 
through  the  coil  changes. 


FIG.  286. 

If  the  coil  be  moved  rapidly  in  front  of  the  magnet,  the 
current  is  stronger,  and  hence  the  E.  M.  F.  must  be  greater 
than  if  it  be  moved  slowly.  Also,  if  the  number  of  turns  of 
wire  be  increased,  the  E.  M.  F.  will  be  increased,  as  will  •  be 
shown  by  the  increased  strength  of  current. 

We  may  continue  our  experiment  still  further  by  inserting 
a  bar  or  disk  of  soft  iron  into  the  coil  and  again  moving  the 
end  of  the  coil  through  the  field  of  force  in  front  of  the  north 
pole  of  the  magnet:  A  very  decided  increase  in  the  strength 
of  current  is  observed.  If,  further,  another  bar  magnet  be 
placed  so  that  its  south  end  faces  the  other  end  of  the  coil, 
and  the  coil  be  fixed  at  its  center  while  its  two  ends  are 
made  to  rotate  past  the  two  poles,  more  lines  of  force  are 
cut  and  greater  E.  M.  F.  is  developed,  as  is  seen  from  the 
increased  strength  of  current.  A  powerful  electro-magnet  is 
preferable  to  a  permanent  magnet  as  an  inducer,  since  its 
strength  or  magnetic  density  can  be  made  much  greater. 

We  have  now  found  that  E.  M.F.  and  strength  of  current 
depend  upon  (1)  the  rapidity  of  motion  of  the  wire  through  the 
field ;  (2)  the  number  of  turns  of  the  wire  ;  and  (3)  the  number 
of  lines  of  force  cut)  or  the  strength  of  the  field. 


338 


ETHER    DYNAMICS. 


DIRECTION  OF  FQRCB 


365.  Rule  for  Determining  the  Direction  of  the  Induced 
Current.  Place  the  right  hand  (Fig.  287)  so  that  the  direction 
of  the  forefinger  coincides  with  the  direction  of  the  lines  of 

force  (as  indicated  by 
«  a   test  -  needle),   and 

the  thumb  points  in 
the  direction  of  motion 
of  the  part  of  the  con- 
ductor under  consid- 
eration ;  the  middle 
finger  will  indicate 
the  direction  of  the  in- 
duced current. 

366,  The  Dynamo. 

We  are  now  prepared 

to  study  the  action  of  the  dynamo.  The  inducing  magnet, 
which  is  commonly  an  electro-magnet,  is  called  the  field  mag- 
net, and  the  coil  or  series  of 
coils  of  wire,  which  is  gener- 
ally made  to  move  in  front 
of  the  poles  of  the  field  mag- 
net, is  called  the  armature. 
The  armature  is  that  part  of 
the  electric  circuit  in  which 
the  E.  M.  F.  is  generated. 
Like  the  battery,  it  may  be 
considered  as  the  source  of 
the  current.  The  number  of 
lines  of  force  passing  through  a  circuit  may  in  general  be 
changed  in  two  ways  :  either  (1)  by  moving  the  circuit 
through  a  field  in  which  the  density  of  the  lines  of  force 
varies,  as  represented  in  Fig.  288  ;  or  (2)  by  rotating  the 
plane  of  the  circuit  so  as  to  change  the  angle  which  it  makes 
with  the  line  of  force,  thus  increasing  or  decreasing  the  num- 


5 

1         - 

\ 

/n 

-H 

! 

\JJ/ 

^T> 

\  s, 

g 

\ 

\U 

=£ 

FIG.  288. 


THE    DYNAMO. 


339 


*#• 


FIG.  289. 


her  which  the  circuit  encloses  (Fig.  289).  A  simple  form  of 
dynamo  is  illustrated  in  Fig.  290.  A  large  core  of  soft  iron 
of  the  U-form,  surrounded  with  a  coil  of  insulated  wire,  and 
terminating  in  the  pole  pieces  N  and  S,  forms  the  field  magnet. 

The  armature  consists  of  a  sin- 

^  __  __  __ 

gle  rectangular  loop  of  wire 
fixed  to  a  horizontal  axis  and 
terminating  in  two  rings  of 
metal,  a  and  b,  which  are 
fixed  to  the  axle,  but  insulated 
from  it. 

When  a  current  passes  through 
the  field  coils,  and  the  core 
becomes  magnetized,  lines  of 
force  cross  and  fill  the  space  between  the  pole  pieces  of  the 
field  magnet.  As  these  lines  are  cut  by  the  horizontal  parts 
of  the  rotating  wire,  an  E.  M.  F.  is  generated  in  these  parts, 
and  a  current  flows  in  the  direction  indicated  by  the  arrows. 

It  is  evident  that 
the  armature  loop 
is  successively 
filled  and  emptied 
with  the  flux  — 
filled  when  its 
plane  is  vertical, 
empty  when  its 
plane  is  horizon- 
tal. 

A  metallic  or 
carbon  brush,  m, 
touches  and  car- 

ries off  the  current  from  the  lower  horizontal  segment  of  the 
rectangular  coil.  This  current  flows  through  the  external 
resistance  R,  and  completes  the  circuit  through  the  brush  n  to 
the  ring  b,  and  the  upper  half  of  the  loop.  The  current  will 


FIG.  290. 


340  ETHER   DYNAMICS. 

continue  to  flow  in  this  direction  while  the  loop  moves 
through  one  half  of  a  revolution.  Since  the  lines  of  force 
are  cut  in  the  opposite  direction  in  the  next  half  revolution, 
the  current  will  be  reversed  in  the  armature  wire  and  also 
through  the  external  circuit.  Thus  with  each  half  revolution 
of  the  armature  a  reversal  of  the  current  takes  place.  This, 
then,  would  be  called  an  alternating  current  dynamo. 

367.  The  Commutator.  The  alternating  current  is  not 
adapted  to  all  uses,  and  for  many  purposes  it  is  neces- 
sary to  have  the  current  continuously  flowing  in  the  same 
direction.  To  accomplish  this  a  commutator  is  attached  to 
the  axis  of  the  armature. 

In  Fig.  291  the  two  brass  rings  (a  and  b,  Fig.  290)  are  replaced  by  a  single 
brass  tube  divided  into  two  parts  by  cutting  it  lengthwise.  These  two 
segments  are  attached  to  but  insulated  from  the  axis,  and  are  connected 

with  the  separate  ends  of  the 
armature  wire.  When  the 
plane  of  the  armature  coil  is 
perpendicular  to  the  line^  of 
force  passing  from  N  to  S,  as 
in  Fig.  291,  no  lines  of  force 

are  being  cut,  and  hence  no 

fr  ,J  E.  M.  F.  is  developed  and  no 

^-^HnToHnnrrax^  current    flows    through    the 

loop.  But  the  instant  it  moves 
out  of  the  vertical  in  the  di- 
rection of  the  arrow,  lines  of  force  will  be  cut,  and  as  the  lower  segment 
of  the  loop  is  moving  upward  past  the  pole  S,  and  the  other  segment  is 
moving  downward  in  front  of  the  pole  N,  a  positive  current  flows  from 
the  loop  through  the  segment  a,  the  brush  m,  the  resistance  R,  the  brush 
n,  and  the  segment  of  the  commutator  b.  During  the  next  half  of  a  revolu- 
tion the  lines  of  force  will  be  cut  from  an  opposite  direction  by  each  of 
the  horizontal  segments  of  the  armature  loop,  and  hence  the  current  will 
be  reversed.  But  the  segment  b  of  the  commutator  will  now  be  in  con- 
tact with  the  brush  m  ;  and  although  the  current  is  reversed  in  the 
armature  it  will  flow  off  at  the  brush  m  as  before.  That  is,  one  of  the 
brushes  is  kept  always  positive  and  the  other  negative,  and  the  current 
flows  from  the  positive  brush  through  the  external  circuit  to  the  negative 


CLASSES    OF    DYNAMOS. 


341 


brush.  Inasmuch  as  no  E.  M.  F.  is  developed  when  the  plane  of  the 
loop  is  perpendicular  to  the  lines  of  force,  it  is  at  this  point  that  the 
brushes  pass  from  one  segment  of  the  commutator  to  the  other. 

Thus,  although  the  current  in  the  armature  is  reversed 
with  each  half  revolution,  by  providing 
that  the  connections  of  the  armature  coil 
shall  be  shifted  at  the  moment  when  the 
current  in  the  coils  is  reversed,  a  reversal 
of  the  current  in  the  external  circuit  is 
prevented.  This  arrangement  constitutes 
a  direct*current  dynamo.  Instead  of  one 
coil  we  may  have  two  or  any  number  of 
coils,  each  separate  from  the  others,  and 
terminating  in  strips  or  segments  which 
are  on  opposite  sides  of  the  commutator. 
Generally  the  coils  are  connected  in  series, 
thus  making  any  segment  a  terminal  of 
one  coil  and  the  beginning  of  the  next. 

368.  Classes  of  Dynamos.1  Dynamos  may  be  divided  into 
different  classes  according  to  the  method 
by  which  their  field  magnets  are  excited. 
Figure  292  illustrates  a  magneto-electric 
machine,  where  the  field  magnet  is  a 
permanent  steel  magnet.  This  form  of 
machine  is  seldom  used,  since  a  perma- 
nent steel  magnet  cannot  be  made  as 
powerful  as  an  electro-magnet  having  a 
soft  iron  core  of  equal  mass. 

Figure  290  illustrates  a  separately  ex- 
cited dynamo,  where  the  field-magnet  coils 
receive    their   currents   from   a   separate 
generator,  e.g.  a  battery,  and  not   from  the  armature  coils. 

1  For  the  characteristics  of  the  various  classes  of  dynamos,  as  well  as  for  a  most 
lucid  and  comprehensive  treatment  of  dynamos  generally,  see  "  Dynamo-Electric 
Machinery,"  by  S.  P.  Thompson. 


342 


ETHER    DYNAMICS. 


Since  an  alternating  current  dynamo  does  not  produce  a  con- 
stant magnetic  field,  alternating  dynamos,  in  general,  are 
separately  excited.  Small  direct-current  dynamos  are  com- 
monly used  to  energize  the  field  magnets  of  alternating 
dynamos.  Such,  for  example,  are  the  Westinghouse  and  the 
Thompson-Houston  incandescent-lighting  dynamos. 

In  a  series  dynamo  the  coils  of  the  field  magnet  are  joined 
in  series  with  the  armature  so  that  the  entire  current  passes 
through  these  coils. 

Figure  293  illustrates  a  shunt  machine,  where  the  field  coil 
serves  as  a  shunt  to  the  external  circuit.  A  is  the  main 
wire,  and  B  is  the  shunt  wire.  In  the  shunt  machine  only  a 
part  of  the  current  generated  in  the  armature  passes  through 


FIG.  294, 


REVERSIBILITY    OF   THE   DYNAMO.  343 

the  field  coils.  Sometimes,  for  purposes  of  regulation,  the  field 
magnet  is  encircled  by  both  series  and  shunt  coils.  Such  dyna- 
mos are  said  to  be  compound  wound.  A  dynamo  is  said  to  be 
"  self-exciting  "  when  the  whole  or  any  part  (Fig.  293)  of  the 
current  which  is  produced  is  used  to  magnetize  the  field  magnets. 

The  cores  of  the  field  magnets  of  a  self-exciting  dynamo, 
after  being  once  excited  from  any  source,  e.g.  another  dynamo, 
always  retain  a  little  residual  magnetism,  so  that  when  the 
armature  begins  to  rotate,  a  slight  current  is  at  once  induced 
in  it.  This  current  flows  around  the  magnets  and  intensifies 
their  power.  This  strengthens  the  field,  and  the  stronger 
field  reacts  to  increase  the  current,  so  that  the  current  soon* 
rises  to  its  normal  strength. 

All  figures  hitherto  have  been  diagrammatic  representations 
of  dynamos.  Fig.  294  represents  one  of  the  most  common 
forms  of  the  Edison  dynamo.  It  is  a  shunt-wound  dynamo. 

SECTION   XV. 
ELECTRIC   MOTOR. 

369.  Reversibility  of  the  Dynamo.  If  a  current  from  an 
external  source,  e.g.  a  battery  or  another  dynamo,  be  passed 
through  the  armature  and  field  magnet  of  a  direct-current 
dynamo,  it  will  excite  the  armature  and  make  of  it  an  elec- 
tro-magnet, and  will  also  excite  the  fields.  The  current  will 
enter  at  the  terminals  and  will  pass  through  the  commu- 
tator into  the  armature.  The  relation  of  parts  is  such  that 
in  doing  this  it  will  develop  N-  and  S-poles  in  parts  of  the 
periphery  of  the  armature  distant  from  the  N-  and  S-poles  of 
the  fields.  Hence,  there  will  be  set  up  between  the  armature 
and  the  poles  of  the  field  magnet  a  stress  tending  to  move  the 
former  a  little  in  the  opposite  direction  to  that  in  which  it  is 
compelled  to  move  when  generating  a  current.  But  as  soon  as 
it  has  turned  a  short  distance  the  action  of  the  commutator 
shifts  the  current,  and  new  poles  are  established  in  the  arm  a- 


344  ETHER   DYNAMICS. 

ture  back  of  the  first  and  in  the  same  relative  positions  which 
they  at  first  occupied.  The  armature  continues  to  rotate  as 
the  new  poles  are  attracted  and  repelled,  and  the  action  goes 
on  so  long  as  a  current  is  supplied.  Obviously,  if  there  were 
no  commutator  the  poles  of  the  armature  would  be  fixed,  and 
it  never  could  rotate  through  a  greater  angle  than  180°. 

It  is  evident,  then,  that  if  two  dynamos  be  connected  by 
wires  in  the  same  circuit  and  the  armature  of  one  be  rotated, 
the  armature  of  the  other  will  rotate  in  a  reverse  direction 
as  soon  as  the  current  transmitted  from  the  first  attains  a 
certain  intensity. 
• 

Let  A  and  B  (Fig.  295)  represent  in  diagram  two  dynamos  constructed 
exactly  alike.     Mechanical  power  is  supplied  to  the  dynamo  A  by  the 


FIG.  295. 

falling  weight  C.  In  this  dynamo  mechanical  energy  is  transformed 
into  the  energy  of  an  electric  current,  which  in  passing  through  B  (now 
acting  as  a  motor)  becomes  again  transformed  into  mechanical  energy 
and  the  weight  D  is  raised  thereby.  The  energy  stored  in  D,  after  it  is 
raised,  plus  some  additional  energy  to  compensate  for  that  lost  in  the 
transmission  from  A  to  B  and  in  the  several  transformations,  may  be 
used  again  by  a  reversal  of  transformations  to  raise  the  weight  C. 

The  dynamo,  then,  is  a  reversible  machine,  in  which 
mechanical  energy  can  be  changed  directly  into  electrical 
energy,  or  electrical  energy  into  mechanical  energy.  When 
the  dynamo  is  used  for  the  latter  transformation,  it  is  com' 


THE    ELECTRIC    RAILWAY. 


345 


monly  known  as  an  electric  motor.  In  other  words,  a  modern 
motor  is  a  dynamo  reversed.  The  discovery  of  the  reversibil- 
ity of  the  dynamo  is  considered  to  be  one  of  high  importance. 

370.  The  Electric  Railway.  The  system  of  electric  car  propul- 
sion consists  in  the  generation  of  an  electric  current  at  some  power 
station  by  means  of  dynamos,  its  transmission  over  conductors  to  the 
electric  motors  on  the  cars,  and  its  transformation  into  mechanical 
energy,  which  gives  motion  to  the  car. 

The  current,  as  shown  by  the  arrows  (Fig.  296),  passes  from  the 
dynamo  D  through  a  switch  board,  S,  with  which  are  connected  a 
current-indicator,  voltmeter,  fuses,  etc.  ;  thence  over  the  trolley  wire  or 


FIG.  296. 


overhead  conductor  A,  apportion  passing  down  through  the  trolley 
arm  T  (the  remainder  going  on  to  supply  other  cars),  along  wires  con- 
cealed in  the  car  to  the  motor,  through  the  motor,  and  thence  through 
the  wheels  to  the  rails,  and  back  to  the  switch  board  and  dynamo. 

In  some  cases  the  rails  connected  by  copper  tie  wires  soldered  to  each 
rail  at  the  joints  serve  for  the  return  circuit ;  in  other  cases  a  "  supplemen- 
tary wire"  laid  between  the  rails  is  used.  In  the  latter  case  each  joint 
on  both  rails  is  connected  with  the  supplementary  wire.  Much  study  is 
now  being  devoted  to  the  problem  of  substituting  a  feed  conductor  laid 
in  a  conduit  buried  beneath  the  road  surface  for  the  overhead  trolley 
wire. 

At  each  end  of  the  car  is  a  "  controller  stand  "  provided  with  a  handle, 
by  means  of  which  the  resistance  through  a  rheostat  may  be  varied,  and 
thereby  the  strength  of  the  current  through  the  motor  and  the  speed  of 
the  car  is  regulated.  There  is  also  a  reversing  switch  by  means  of 
which  the  direction  of  the  rotation  of  the  armature  may  be  changed  and 


346  ETHER    DYNAMICS. 

thereby  the  motion  of  the  car  quickly  checked  in  the  case  of  emergency, 
or  the  motion  may  be  reversed. 


FIG.  297. 


Each  car  usually  has  two  motors  connected  in  multiple,  and  each 
motor  is  geared  to  its  own  car  axle.  Fig.  298  represents  one  half  of 
a  car  truck,  with  its  motor,  gearing,  etc. 


SECTION   XVI. 
SECONDARY    OR    STORAGE   BATTERIES. 

371,  Reversibility  of  Electrolysis.  If  water  be  decom- 
posed for  a  time  between  neutral  electrodes  such  as  platinum 
plates,  and  then  the  battery  or  other  generator  be  withdrawn 
from  the  circuit  and  replaced  by  a  sensitive  galvanometer,  a 
deflection  of  the  needle  shows  that  a  transitory  current  flows 
in  the  opposite  direction  to  the  primary  or  electrolyzing  cur- 
rent. It  is  evident  that  the  electrolyzing  current  polarizes 
the  electrodes  in  the  electrolyte,  and  that  energy  is  thus 


REVERSIBILITY    OF    ELECTROLYSIS.  347 

stored  in  the  cell.  Polarization  is  of  the  nature  of  a  counter 
E.  M.  F.  It  is  precisely  this  polarization  which  we  have  to 
contend  with  in  nearly  all  voltaic  cells,  and  which  we  seek 
to  neutralize  by  means  of  depolarizing  substances. 

Devices  for  thus  storing  up  energy  by  electrolysis  are 
called  storage  or  secondary  batteries,  and  sometimes  accumu- 
lators. Note  that  the  process  is  an  electrical  storage  of  energy, 
not  a  storage  of  electricity.  The  energy  of  the  charging  cur- 
rent is  transformed  into  the  potential  energy  of  chemical 
separation  in  the  storage  cell.  When  the  circuit  of  the  stor- 
age cell  is  closed  this  energy  is  reconverted  into  the  energy 
of  an  electric  current  in  precisely  the  same  way  as  with 
an  ordinary  voltaic  cell. 

A  common  form  of  storage  cell  consists  of  a  series  of  lead  plates  cast 
in  the  form  of  a  framework  of  bars  at  right  angles  to  one  another,  as 
shown  in  Fig.  298.  The  spaces  be- 
tween the  bars  of  the  positive  plates 
are  filled  with  a  paste  of  red  lead 
and  sulphuric  acid  ;  the  spaces  in  the 
negative  plates  are  filled  with  a  paste 
of  litharge  and  sulphuric  acid.  The 
liquid  surrounding  the  plates  is  dilute 
sulphuric  acid.  The  positive  plates 
are  all  connected  in  multiple  at  one 
end  of  the  cell,  and  the  negative 
plates  are  connected  at  the  other  FIG.  298. 

end.      The  cell  is  charged  by  con- 
necting a  dynamo  with  its  terminals,  when  the  positive  plates  become 
peroxidized  by  electrolysis  and  the  negative  plates  deoxidized. 

The  storage  battery  offers  a  means  of  accumulating  energy  at  one  time 
or  place,  and  using  it  at  some  other  time  or  place.  For  example,  energy 
of  a  dynamo  current  may  be  stored  during  the  daytime  when  the  current 
is  not  needed  for  illuminating  purposes ;  and  this  energy,  reconverted 
into  electric  energy,  may  feed  incandescent  lamps  at  night  at  any  con- 
venient place  ;  or  the  charged  cells  may  be  transported  to  lecture  halls, 
workshops,  electric  cars,  etc.,  where  powerful  currents  may  be  needed. 

A  storage  cell  has  an  E.  M.  F.  of  2.2  volts  or  more.  Its  resistance 
depends  on  the  size  and  number  of  plates,  but  is  not  usually  greater  than 
.005  ohm. 


348 


ETHER    DYNAMICS. 


SECTION    XVII. 
THERMO-ELECTRIC    CURRENTS. 

372.  Heat    Energy    Transformed    Directly    into    Electric 
Energy. 

Experiment.     Let  G   (Fig.   299)  be  a  low-resistance,  astatic-needle 
galvanometer.      Form  two  junctions  between  its  copper-wire  terminals 

and  an  iron  wire  by  tightly  twisting  the 
wires  together  near  their  extremities.  Let 
A  and  B  be  the  two  junctions.     Immerse 
both   junctions  in   separate    beakers   of 
water.      (1)  Raise  the  water  in  one  of 
the  beakers  to  the  boiling  point  ;  a  cur- 
rent passes  through  the  galvanometer  G, 
causing  a  deflection   (say)  to  the  right. 
(2)  Reverse  the  position  of  the  two  beak- 
ers of  water  ;  the  current  now  causes  a  reversed  deflection.     (3)  Bring 
the  cold  water  to  the  boiling  point ;  the  deflection  diminishes  steadily  to 
zero  as  the  difference  in  temperature  in  the  two  waters  diminishes. 

Thus,  the  thermo-electric  current  depends  on  the  difference 
of  temperature  of  the  junctions,  vanishing  when  that  differ- 
ence vanishes.      Suppose  the  junctions  to  be  at  10°  C.  and 
100°  C.,  the  E.  M.  F.  will  be  about  .0015  volt. 
It  would   require    about  1000   pairs    of   such 
junctions  to    give  an   E.  M.  F.  comparable  to 
that  of  an  ordinary  voltaic  cell. 


FIG.  299. 


373.  Thermo-electric  Batteries  and  Thermo- 
piles. The  E.  M.  F.  may  be  built  up  by  com- 
bining a  large  number  of  pairs  with  one 
another  in  series.  This  is  done  on  the  same 
principle  and  in  the  same  manner  that  voltaic  pairs  are 
united,  viz.  by  joining  the  +  metal  of  one  part  to  the  — 
metal  of  another.  Fig.  300  represents  such  an  arrangement. 
The  light  bars  are  bismuth  and  the  dark  ones  antimony. 
If  the  source  of  heat  be  strong  and  near,  one  face  may  be 


ELECTRIC    LIGHT  ;     VOLTAIC    ARC.  349 

heated  much,  hotter  than  the  other,  and  a  current  equal 
to  that  from  an  ordinary  galvanic  cell  is  often  obtained. 
Such  contrivances  for  generating  electric  currents  are  called 
thermo-electric  batteries.  They  are  seldom  used,  inasmuch  as 
the  best  of  them  transform  less  than  one  per  cent  of  the  heat* 
energy  given  out  by  the  source  of  heat.  Furthermore,  the 
E.  M.  F.  of  thermic  piles  is  generally  so  small  that  any 
considerable  external  resistance  makes  the 
current  extremely  weak.  If  the  source  of 
heat  be  feeble  or  distant,  the  feeble  cur- 
rent may  serve  to  measure  the  difference 
of  temperature  between  the  ends  "of  the 
bars  turned  toward  the  heat  and  the  other 
ends,  which  are  at  the  temperature  of  the 
air.  The  apparatus,  when  used  for  this 
purpose,  is  called  a  thermopile  or  thermo- 
multiplier.  A  combination  (Fig.  301)  of  FIG.  301. 

as  many  as  thirty-six  pairs  of  antimony 
and  bismuth  bars,  connected  with  a  very  sensitive  galva- 
nometer, constitutes  an  exceedingly  delicate  thermoscope  and 
thermometer.  Changes  of  temperature  that  would  not  produce 
a  perceptible  variation  in  an  ordinary  thermometer  can,  by  the 
use  of  a  thermo-electric  pile,  be  made  to  produce  large  deflec- 
tions of  the  galvanometer  needle.  Kadiations  from  the  body' 
of  an  insect  several  inches  from  the  pile  may  cause  a  sensible 
deflection. 

SECTION   XVIII. 
THE   ELECTRIC    LIGHT. 

374.  Electric  Light;  Voltaic  Arc.  If  the  terminals  of 
wires  from  a  powerful  dynamo  or  galvanic  battery  be 
brought  together,  and  then  separated  1  or  2  mm.,  the  current 
does  not  cease  to  flow,  but  volatilizes  a  portion  of  the  ter- 
minals. The  vapor  formed  becomes  a  conductor  of  high 


350 


ETHER    DYNAMICS. 


resistance,  and,  remaining  at  a  very  high  temperature,  pro- 
duces intense  light.  The  heat  is  so  great  that  it  fuses  the 
most  refractory  substances.  Metal  terminals  quickly  melt 
and  drop  off  like  tallow,  and  thereby  become  so  far  sepa- 
rated that  the  electro-motive  force  is  no  longer  sufficient 
for  the  increased  resistance,  and  the  light  is  extinguished. 
Hence,  pencils  of  carbon  (prepared  from  the  coke  deposited 
in  the  distillation  of  coal  inside  of 
gas  retorts),  being  less  fusible,  are 
used  for  terminals. 

The  light  is  too  intense  to  admit  of 
examination  with  the  naked  eye  ;  but 
if  an  image  of  the  terminals  be  thrown 
on  a  screen  by  means  of  a  lens  or  a 
pin  hole  in  a  card,  an  arch-shaped  light 
is  seen  extending  from  pole  to  pole, 
as  shown  in  Fig.  302. 

The  heated  air  containing  the  glow- 
ing particles  of  carbon  forms  what  is 
called  the  electric  arc. 

The  larger  portion  of  the  light,  how- 
ever, emanates  from  the  tips  of  the 
two  carbon  terminals,  which  are  heated 
to  an  intense  whiteness,  although  some 
emanates  from  the  arc.  The  -f-  pole  is 
hotter  than  the  —  pole,  as  is  shown  by 
its  glowing  longer  after  the  current  is 
stopped.  The  carbon  of  the  +  pole 
becomes  volatilized,  and  the  light-giving  particles  are  trans- 
ported from  the  +  pole  to  the  —  pole,  forming  a  bridge  of 
luminous  vapor  between  the  poles.  What  we  see  is  not  elec- 
tricity, but  luminous  matter. 


FIG.  302. 


375,  Electric  Lamp.      It   is    apparent   that   the  4-  pole   is 
subject  to  a  wasting  away  ;  so  also  the  —  pole  wastes  away, 


ELECTRIC   LAMPS. 


351 


but  not  so  fast.     At  the  point  of  the  former  a  conical-shaped 

cavity  is  formed,  while  around  the  point  of  the  latter  warty 

protuberances   appear.     When,  in   consequence 

of  the  wearing  away  of  the  -j-  pole,  the  distance 

between  the  two  pencils  becomes  too  great  for 

the  electric  current  to  span,  the  light  goes  out. 

Numerous  self-acting  regulators  for  maintaining 

a  uniform  distance  between  the  poles  have  been 

devised.     Such    an   arrangement   (Fig.  303)    is 

called  an  electric  lamp.     The  movements  of  the 

carbons  are  accomplished  automatically  by  the 

action  of  the  current  itself. 

376.  Incandescent  Electric  Lamps.  The  in- 
candescent (or  "  glow  ")  light  is  produced  by  the 
heating  of  some  refractory  body  to  a  state  of 
incandescence  by  the  passage  of  an  electric  cur- 
A  rent.  Carbon  filaments  are 

now  almost  exclusively  used 
in  incandescent  lamps.  The 
filament  of  the  Edison  lamp 
is  carbonized  bamboo.  It  is 
essential  that  the  oxygen  of  the  air  be 
removed  from  these  bulbs,  otherwise  the 
carbons  would  be  quickly  burned  out ; 
hence,  very  high  vacua  are  produced  in 
the  bulbs  with  a  mercury  pump. 

Fig.  304  represents  an  Edison  lamp.  The  loop 
or  filament  of  carbon  L  is  joined  at  n  n  to  two 
platinum  wires,  which  pass  through  the  closed 
end  of  the  glass  tube  T.  One  of  these  wires  is  con- 
nected with  the  brass  ring  B,  and  the  other  with 
the  brass  button  D,  at  the  bottom  of  the  lamp. 
When  the  lamp  is  screwed  into  its  socket,  connection  is  made  with  the 
line  through  pieces  of  brass  in  the  socket,  which  are  insulated  from  each 
other. 


FIG.  303. 


352 


ETHER    DYNAMICS. 


An  Edison  16-candle-power  lamp  has  a  resistance  (when  hot)  of  about 
140  ohms,  the  difference  of  potential  at  its  terminals  is  about  110  volts, 

and  it  requires  a  current  of  0.75 
ampere.  Each  lamp  consumes 
about  one  tenth  of  a  horse- 
power, or  about  4  watts  per 
candle-power.  One  kilo-watt 
(1  k.w.  =  1.34  h.p.)  hour  will 
supply  sixteen  16-candle-power 
lamps  for  one  hour,  and  give  as 
FlG  305  much  light  as  100  cubic  feet  of 

gas. 

Incandescent  lamps  are  usually  introduced  into  the  circuit  in  multiple 
arc  (Fig.  305),  the  current  being  equally  divided  by  properly  regulating 
the  resistance  between  all  the  lamps  in  the  circuit. 


SECTION   XIX. 
ELECTROTYPING   AND    ELECTROPLATING. 

377.  Electrotyping.  This  book  is  printed  from  electrotype 
plates.  A  molding-case  of  brass,  in  the  shape  of  a  shallow 
pan,  is  filled  to  the  depth  of  about  one  quarter  of  an  inch  with 
melted  wax.  A  few  pages  are  set  up  in  common  type,  and  an 
impression  or  mold  is  made  by  pressing  these  into  the  wax. 
The  type  is  then  distributed,  and  again  used  to  set  up  other 
pages.  Powdered  plumbago  is  applied  by  brushes  to  the  sur- 
face of  the  wax  mold  to  render  it  a  conductor.  The  case  is 
then  suspended  in  a  bath  of  copper  sulphate  dissolved  in 
dilute  sulphuric  acid.  The  —  electrode  of  a  galvanic  battery 
or  dynamo  machine  is  applied  to  it,  and  from  the  -+-  electrode 
is  suspended  in  the  bath  a  copper  plate  opposite  and  near  to 
the  wax  face.  The  salt  of  copper  is  decomposed  by  the  elec- 
tric current,  and  the  copper  is  deposited  on  the  surface  of  the 
mold.  The  sulphuric  acid  appears  at  the  -f  electrode,  and,  com- 
bining with  the  copper  of  this  electrode,  forms  new  molecules 
of  copper  sulphate.  When  the  copper  film  has  acquired  about 
the  thickness  of  an  ordinary  visiting  card,  it  is  removed  from 


ELECTROPLATING.  353 

the  mold.  This  shell  shows  distinctly  every  line  of  the 
types  or  engraving.  It  is  then  backed,  or  filled  in,  with 
melted  type-metal,  to  give  firmness  to  the  plate.  The  plate 
is  next  fastened  on  a  block  of  wood,  and  thus  built  up  type- 
high,  and  is  now  ready  for  the  printer.  (For  full  directions 
which  will  enable  a  pupil  to  electrotype  in  a  small  way,  see 
the  author's  "  Physical  Technics.") 


FIG.  306. 

378,  Electroplating.  The  distinction  between  electroplat- 
ing and  electrotyping  is  that  with  the  former  the  metallic 
coat  remains  permanently  on  the  object  on  which  it  is  depos- 
ited, while  with  the  latter  it  is  intended  to  be  removed.  The 
processes  are,  in  the  main,  the  same.  The  articles  to  be 
plated  are  first  thoroughly  cleaned,  and  suspended  on  the 
-  electrode  of  a  battery,  and  then  a  plate  of  the  same  kind  of 
metal  that  is  to  be  deposited  on  the  given  articles  is  sus- 
pended from  the  -f  electrode  (Fig.  306).  The  bath  used  is  a 
solution  of  a  salt  of  the  metal  to  be  deposited.  The  cyanides 
of  gold  and  silver  are  generally  used  for  gilding  and  silvering. 


354  ETHER    DYNAMICS. 

SECTION   XX. 

THE    ELECTRIC    TELEGRAPH. 

379,  Morse  Telegraph,      First,   it   should   be   understood 
that,  instead  of  two  lines  of  wires  (one  to  convey  the  electric 
current  far  away  from  the  battery,  and  another  to  return  it 
to  the  battery),  if  the  distant  pole  be  connected  with  a  large 
metallic  plate  buried  in  moist  earth,  or,  still  better,  with  a 
gas  or  water  pipe  that  leads  to  the  earth,  and  the  other  pole 
near  the  battery  be  connected  in  like  manner  with  the  earth, 
so  that  the  earth  forms  about  one  half  of  the  circuit,  there 
will  be  needed  only  one  wire  to  connect  telegraphically  two 
places  that  are  distant  from  each  other. 

Let  B  (Fig.  307,  Plate  II)  represent  the  message  sender,  or  operator's 
key  ;  Y,  the  message  receiver.  It  may  be  seen  that  the  circuit  is  broken 
at  B.  Let  the  operator  press  his  ringer  on  the  knob  of  the  key.  He 
closes  the  circuit,  and  the  electric  current  instantly  fills  the  wire  from 
Boston  to  New  York.  It  magnetizes  a  ;  a  draws  down  the  lever  b,  and 
presses  the  point  of  a  style  on  a  strip  of  paper,  c,  that  is  drawn  over  a 
roller.  The  operator  ceases  to  press  upon  the  key,  the  circuit  is  broken, 
and  instantly  b  is  raised  from  the  paper  by  a  spiral  spring,  d.  Let  the 
operator  press  upon  the  key  only  for  an  instant,  or  long  enough  to  count 
one  ;  a  simple  dot  or  indentation  will  be  made  in  the  paper.  But  if  he 
press  upon  the  key  long  enough  to  count  three,  the  point  of  the  style  will 
remain  in  contact  with  the  paper  the  same  length  of  time  ;  and,  as  the 
paper  is  drawn  along  beneath  the  point,  a  short  straight  line  is  produced. 
This  short  line  is  called  a  dash.  These  dots  and  dashes  constitute  the 
alphabet  of  telegraphy. 

380.  The  Sounder.    If  the  strip  of  paper  be  removed,  and  the  style 
be  allowed  to  strike  the  metallic  roller,  a  sharp  click  is  heard.     Again, 
when  the  lever  is  drawn  up  by  the  spiral  spring  it  strikes  a  screw  point 
above  (not  represented  in  the  figure),  and  another  click,  differing  slightly 
in  sound  from  the  first,  is  heard.     A  listener  is  able  to  distinguish  dots 
from  dashes  by  the  length  of  the  intervals  of  time  that  elapse  between 
these  two  sounds.     Operators  generally  read  by  ear,  giving  heed  to  the 
clicking  sounds  produced  by  the  strokes  of  a  little  hammer.     A  receiver 
so  used  is  called  a  sounder,  a  common  form  of  which  is  represented  in 
the  lower  central  part  of  Plate  II. 


355 


gg 


356  ETHER    DYNAMICS. 

381.  The  Relay.     The   strength   of  the  current  is  diminished,  of 
course,  as  the  line  is  extended  and  the  number  of  instruments  in  the  cir- 
cuit is  increased.     Hence,  a  battery  that  would  give  a  current  sufficient 
to  move  the  parts  of  a  single  sounder  audibly  on  a  short  line  would  not 
move  the  same  parts  of  many  sounders  on  a  long  line  with  sufficient 
force  to  render  the  message  audible.     Resort  is  had  to  relays. 

In  Fig.  308,  Plate  II,  R  represents  a  relay  and  S  a  sounder.  Suppose 
a  weak  current  arrives  at  New  York  from  Boston,  and  has  sufficient 
strength  to  attract  the  armature  of  the  relay  at  that  station.  This,  as 
may  be  seen  by  examination  of  the  diagram,  will  close  another  short 
circuit,  called  the  local  circuit,  and  send  a  current  from  a  local  battery 
located  in  the  same  office  through  the  sounder  at  that  station.  The 
sounder,  being  operated  by  a  battery  in  a  circuit  of  only  a  few  feet  in 
length,  delivers  the  message  audibly. 

SECTION   XXI. 
THE   TELEPHONE. 

382.  Bell  Telephone.    Fig.  309  represents  a  sectional  and  a  per- 
spective view  of   this  instrument.      It  consists  of  a  steel   magnet,  A, 
encircled  at  one  extremity  by  a  spool  of  very  fine  insulated  wire,  B,  the 
ends  of  which  are  connected  with  the  binding  screws  D  D.     Immediately 
in  front  of  the  magnet  is  a  thin  circular  iron  disk,  E  E.     The  whole  is 
enclosed  in  a  wooden  or  rubber  case,  F.     The  conical-shaped  cavity  G 
serves  the  purpose  of  either  a  mouthpiece  or  an  ear-trumpet,     There  is 
no  difference  between  the  transmitting  and  the  receiving  telephone  ;  con- 
sequently, either  instrument  may  be  employed  as  a  transmitter,  while 
the  other  serves  as  a  receiver.     Two  magneto  telephones  in  a  circuit  are 
virtually  in  the  relation  of  a  dynamo  and  a  motor.     The  transmitter 
being  in  itself  a  diminutive  dynamo,  no  battery  is  required  in  the  circuit. 
Connect  in  circuit  two  such  telephones,  and  the  apparatus  is  ready  for 
use. 

A  person  talking  near  the  disk  of  the  transmitter  throws  it  into  rapid 
vibration.  The  disk,  being  quite  close  to  the  magnet,  is  magnetized  by 
induction  ;  and  as  it  vibrates  its  magnetic  power  is  constantly  changing, 
being  strengthened  as  it  approaches  the  magnet  and  enfeebled  as  it 
recedes.  This  fluctuating  magnetic  force  will  of  course  induce  currents 
in  alternate  directions  in  the  neighboring  coil  of  wire.  These  currents 
traverse  the  whole  length  of  the  wire,  and  so  pass  through  the  coil  of  the 
distant  instrument.  When  the  direction  of  the  arriving  current  is  such 
as  to  increase  the  intensity  of  the  magnetic  field  of  the  receiver,  the 


BELL   TELEPHONE. 


357 


magnet  attracts  the  iron  disk  in  front  of  it  more  strongly  than  before. 
When  the  current  is  in  the  opposite  direction,  the  disk  is  less  attracted, 
and  flies  back.  Hence,  the  disk  of  the  receiving  telephone  is  forced  to 
repeat  whatever  movement  is  imparted  to  the  disk  of  the  transmitting 


FIG.  309. 


telephone.    The  vibrations  of  the  former  disk  generate  sound-waves  in  the 

same  manner  as  the  vibrations  of  a  tuning  fork  or  of  the  head  of  a  drum. 

The  above  is  a  description  of  the  original  and  simplest  form  of  the 

Bell  telephone.     It  is  apparent  that  the  original  energy  (i.e.  that  of  the 


Line  Wire 


PIG. 310. 


voice)  applied  at  the  transmitter  must,  during  its  successive  transforma- 
tions, and  especially  during  its  transmission  in  the  form  of  electric  energy 
through  large  resistances,  become  very  much  enfeebled,  so  that  when  it 


358 


ETHER    DYNAMICS. 


Ground  W 


Line  Wire 


reappears  as  sound,  the  sound  is  quite  feeble  and  frequently  inaudible. 
The  first  grand  improvement  on  the  original  consists  in  introducing  a 
battery  into  the  circuit,  and  so  arranging  that  the  voice,  instead  of  being 

obliged  to  generate  currents,  shall  be  re- 
quired only  to  render  a  current,  already 
generated  by  a  voltaic  cell,  fluctuating  or 
undulating. 

The  fluctuations  are  caused  by  a  vary- 
ing resistance  in  the  circuit.  The  pupil 
must  have  learned  by  experience  ere  this 
that  the  effect  of  a  loose  contact  between 
any  two  parts  of  a  circuit  is  to  increase  the 
resistance  and  thereby  weaken  the  current ; 
but  the  effect  of  a  slight  variation  in  pres- 
sure is  especially  noticeable  when  either 
or  both  of  the  parts  are  carbon.  Fig.  310 
illustrates  a  simple  telephonic  circuit  in 
which  are  included  two  variable  resistance 
transmitters,  T  T,  and  two  batteries,  B  B. 
One  of  the  electrodes,  a  platinum  point, 
touches  the  center  of  the  transmitter  disk 
d  ;  the  other  electrode,  a  carbon  button,  a, 
is  pressed  by  a  spring  gently  against  the 
platinum  point.  Every  vibration  of  the 
disk,  however  minute,  causes  a  variation 
in  the  pressure  between  the  two  electrodes 

and  a  corresponding  variation  in  the  circuit  resistance.  As  the  resistance 
changes,  so  changes  the  current  strength,  and  thus  the  current  is  rendered 
undulatory. 

The  next  improvement  of  considerable  importance  consists  in  the 
adoption  of  an  induction  coil  (Fig.  310), 
which,  we  have  learned,  may  produce 
a  current  of  much  greater  electro- 
motive force  than  is  possessed  by  the 
original  battery  current.  Since  the 
battery  current  traverses  only  a  local 
circuit,  as  may  be  seen  by  reference  to 
Fig.  310,  a  single  Leclanche"  cell  is 
generally  sufficient  to  operate  it.  The 
currents  induced  by  the  fluctuating  pri- 
mary current  traverse  the  line  wire  and  generate  sonorous  vibrations  in  the 
disk  of  the  receiver  R  in  the  same  manner  as  in  the  original  telephone. 


FIG.  311. 


FIG.  312. 


MAXWELL'S  THEORY  OF  LIGHT. 


359 


Fig.  311  represents  the  entire  telephonic  apparatus  required  at  any 
single  station.  The  box  A  contains  a  small  hand  dynamo,  such  as  is 
represented  in  Fig.  312.  A  person  turning  the  crank  F  generates  a  current 
which  rings  two  pairs  of  electric  bells,  one  pair  (G)  at  his  own  and  another 
pair  at  a  distant  station,  and  thus  attracts  attention.  He  next  takes  the 
receiver  B  off  the  supporting  hook  and  places  it  at  his  ear.  When  the 
weight  is  removed  from  the  hook,  the  hook  rises  a  little  and  throws 
the  dynamo  and  bells  out  of  the  circuit,  and  at  the  same  time  introduces 
the  receiver  B,  the  transmitter  C,  and  the  battery  D,  so  that  the  circuit 
stands  as  represented  in  Fig.  310.  E  is  a  "  lightning  arrester." 

In  Fig.  313,  A  and  B  are  buttons  of  carbon ;  the  former  is  attached  to 
a  thin  iron  disk,  the  latter  to  a  steel  spring,  C,  and  both  are  connected  in 
circuit  with  a  battery  and  a  tele- 
phone used  as  a  receiver.  The 
spring  presses  B  against  A,  and 
any  slight  jar  will  cause  a  varia- 
tion in  the  pressure  and  corre- 
sponding variations  in  the  cur- 
rent strength.  D  is  an  induction 
coil. 

By  means  of  this  instrument, 
called  the  microphone,  any  little 
sounds,  as  its  name  indicates, 
such  as  the  ticking  of  a  watch 
or  the  footfall  of  an  insect,  may  be  reproduced  at  a  considerable  distance, 
and  be  as  audible  as  though  the  original  sounds  were  made  close  to  the 
ear. 


PIG.  313. 


SECTION   XXII. 

ELECTRO-MAGNETIC    THEORY    OF    LIGHT. 
RADIATION. 


ELECTRIC 


383.  Maxwell's  Theory  of  Light.  In  1865  Maxwell  pro- 
pounded the  theory  that  light  is  the  result  of  electro-magnetic 
disturbances  of  rapidly  alternating  character  in  the  ether, 
such  as  would  result  from  its  being  set  in  local  strains  and 
being  released  from  them  ;  that  the  vibrations  which  con- 
stitute light  are  electrical  vibrations,  and  that  light-waves 
are  electro-magnetic  waves. 


360  ETHER   DYNAMICS. 

The  Maxwellian  theory  of  light  may  now  be  considered  as 
completely  verified  by  the  wonderful  experimental  researches 
made  by  the  late  Dr.  Hertz.1  "  So  that  we  have  now  a  real 
undulatory  theory  of  light,  no  longer  based  on  an  analogy 
with  sound.  The  whole  domain  of  Optics  is  now  annexed  to 
Electricity,  which  has  thus  become  an  imperial  science."  - 
LODGE. 

The  importance  of  these  experiments  in  a  scientific  sense 
can  scarcely  be  overestimated,  in  so  far  as  they  teach  us  to 
refer  electrostatic  and  electro-magnetic  phenomena  to  the 
intervention  of  the  same  all-pervading  medium.  This  medium 
forms  the  vehicle  by  which  energy  passes  through  space  from 
one  body  to  another,  and  the  source  to  which  we  now  must 
probably  look  for  a  knowledge  of  facts  concerning  the  ultimate 
constitution  of  matter.2  The  term  radiant  energy  is  contin- 
ually acquiring  new  scope  in  physics.3 

1  See  Hertz's  Researches  on  Electrical  Oscillations,  "  Smithsonian  Report,"  1889. 
Hertz  showed  experimentally  that  the  electrical  ether  is  wonderfully  like,  if  not 

identical  with,  the  ether  which  transmits  light  waves.  By  rapidly  charging  and  dis- 
charging a  conductor  he  causes  the  ether  upon  it  to  surge  to  and  fro.  This  agitates 
the  surrounding  dielectric  ether,  and  the  disturbance  travels  in  waves.  The  speed  of 
these  waves  he  determines  to  be  the  same  as  the  speed  of  light-waves.  He  finds  that 
these  waves  may  interfere,  may  be  reflected  from  metal  mirrors,  may  be  refracted 
by  lenses  and  prisms,  and  are  susceptible  of  diffraction  effects.  He  has  shown  that 
many  optical  experiments  can  be  electrically  performed  by  substituting  dielectrics 
for  transparent  bodies,  and  conductors  for  opaque  bodies. 

2  "  Matter  is  the  rotating  parts  of  an  inert  perfect  fluid  which  fills  all  space."  — 
LORD  KELVIN. 

8  A  prophecy.  "  The  conclusions  at  which  we  have  arrived,  that  light  is  an  elec- 
trical distui'bance,  and  that  light-v/aves  are  excited  by  electric  oscillations,  must 
ultimately,  and  may  shortly,  have  a  practical  import.  Our  present  systems  of  mak- 
ing light  artificially  are  wasteful  and  ineffective."  (It  is  estimated  that  not  more 
than  5  per  cent  of  the  energy  put  into  an  incandescent  lamp  is  useful  for  illumina- 
tion.) "  We  want  a  certain  range  of  oscillation  between  400  and  700  trillion  vibra- 
tions per  second  ;  no  other  is  useful  to  us,  because  no  other  has  any  effect  on  our 
retina ;  but  we  do  not  know  how  to  produce  vibrations  at  this  rate.  .  .  .  We  want 
a  small  range  of  rapid  vibrations,  and  we  know  no  better  than  to  make  the  whole 
series  leading  up  to  them.  It  is  as  though,  in  order  to  sound  some  little  shrill  octave 
of  pipes  in  an  organ,  we  were  obliged  to  depress  every  key  and  every  pedal,  and  to 
blow  a  young  hurricane."  — LODGE.  The  production  of  light  by  very  rapidly  alter- 
nating currents  seems  to  give  promise  of  success  in  this  direction.  (See  §  386.) 


RADIOGRAPHY. 


361 


Battery 


SECTION   XXIII. 

THE   RONTGEN   PHENOMENA. 

384.  Radiography,  If  a  glass  bulb  be  exhausted  to  ap- 
proximately one  one-millionth  of  an  atmosphere,  a  condition 
of  things  is  attained  such  as  was  investigated  and  described 
by  Crookes  in  1879.  The  mean  free  path  of  the  residual  gas 
molecules  in  this  bulb  is  greater  than  the  dimensions  of  a  bulb 
of  ordinary  size.  Gas  in  this  state  was  called  by  Crookes 
radiant  matter,  since,  when 
under  the  influence  of  an 
electric  discharge,  it  presents 
properties  quite  different 
from  those  of  ordinary  gas. 

The  molecules  of  gas  are 
strongly  attracted  to  the 
cathode  or  negative  terminal 
of  the  bulb,  where,  becoming 
negatively  electrified,  they 
are  repelled  with  great  force. 
They  travel  in  straight  lines 
till  they  strike  the  walls  of 
the  bulb  or  other  surface 
placed  athwart  their  path. 
This  molecular  bombard- 
ment causes  the  surface  which  receives  the  blows  to  glow 
more  or  less  brilliantly  with  a  color  depending  on  the  sub- 
stance which  receives  the  impact.  These  molecular  streams 
are  known  as  the  cathode  rays  of  a  Crookes  tube. 

The  usual  method  of  exciting  these  bulbs  is  to  connect 
them  by  wires  to  the  terminals  of  the  secondary  of  an  ordi- 
nary induction  coil,  or  to  the  conductors  of  a  Holtz  machine. 

Let  A  (Fig.  314)  represent  an  exhausted  glass  bulb.  Sealed  into  this 
bulb  are  the  electrodes  a  and  b  ;  the  former  usually  consists  of  a  concave 


FIG.  314. 


362  ETHBR   DYNAMICS. 

disk  of  aluminum,  and  the  latter  of  a  flat  disk  of  platinum.  Let  a  be 
connected  to  the  negative  and  b  to  the  positive  pole  of  an  induction  coil. 
The  discharge  consists  of  faint  streamers  which  proceed  in  straight  lines 
from  the  negative  electrode,  as  indicated  in  the  figure.  These  streamers 
are  the  cathode  rays. 

Rontgen  (1895)  accidentally  discovered  that  a  non-lumi- 
nous radiation  emanates  from  an  excited  Crookes  bulb,  and 
after  passing  through  certain  kinds  of  matter  quite  opaque  to 
light,  is  capable  of  producing  photographic  effects  beyond. 
He  with  others  discovered  that  numerous  substances,  such  as 
metals,  glass,  and  bone,  are  rather  opaque  to  the  new  form 
of  radiation  ;  while  many  other  substances,  notably  wood, 
paper,  flesh,  and  rubber,  are  relatively  transparent.  The  eye 
is  quite  insensitive  to  these  rays.  It  soon  became  possible 
to  produce  shadow  pictures  of  the  bones  of  the  body,  as  shown 
in  Plate  III.  Bontgen  called  the  new  radiation  the  X-rays, 
since  he  was  unable  to  state  its  nature.  No  satisfactory 
theory  of  Eiontgen  radiance  has  yet  been  given.  His  dis- 
covery, however,  opens  up  a  vast  new  field  for  experimental 
research,  and  is  likely  to  lead  to  more  definite  views  concern- 
ing the  nature  of  the  ether.  In  the  bulb  the  cathode  ray 
energy  probably  is  transformed  into  X-ray  energy  at  the 
points  of  impact  on  the  platinum  disk. 

The  principal  effects  of  X-rays  by  which  we  are  made  aware 
of  their  existence  are  as  follows  :  (1)  They  affect  a  silver 
salt  on  a  photographic  dry  plate.  (2)  They  make  a  fluo- 
rescent l  substance  shine.  (3)  They  cause  an  electrical  charge 
to  leak  away,  however  well  insulated  it  may  be.  The  last 
property  affords  one  of  the  most  delicate  tests  of  their  pres- 
ence. The  discharge  occurs  whether  the  body  be  positively 
or  negatively  electrified.  The  leakage  takes  place  not  only 
when  the  body  is  surrounded  by  air,  but  also  when  it  is 
imbedded  in  a  solid  non-conductor.  Hence,  any  substance 
when  exposed  to  their  action  becomes  a  conductor. 

1  Fluorescence  is  a  property  which  certain  substances  possess  of  becoming  self- 
luminous  after  exposure  to  the  action  of  light-rays. 


PLATE  III. 


RADIOGRAPH    OF   THE    NORMAL    HUMAN    FOOT. 

[Taken  by  Dr.  A.  W.  Goodspeed.] 


FLUOROSCOPE.  363 

385.  Fluoroscope.    A  very  important  accessory  to  the  appara- 
tus described  above  is  an  instrument  called  a  fluoroscope.     It 
consists  of  a  box  (Fig.  315),  dark  in 

the  interior,  with  an  opening  at  one 
end,  A,  into  which  to  look.  At  the 
opposite  and  larger  end  B  is  spread 
some  fluorescent  material,  prefer- 
ably barium  platinum  cyanide.  Any 
body  which  is  opaque  to  X-rays, 
if  placed  outside  the  fluorescent 
screen,  and  between  it  and  the 
Crookes  bulb,  casts  upon  the  screen 
a  shadow  which  may  be  viewed  by 
looking  in  at  the  opening ;  for  ex- 
ample, one  can  see  a  shadow  picture  of  the  bones  of  his  own 
hand  upon  the  screen,  which  is  elsewhere  illuminated  by  the 
X-rays. 

SECTION  XXIV. 

ALTERNATING   CURRENTS. 

386.  Tesla's  Investigations.1     Of  the  various  branches  of 
electrical  investigation  now  in  progress  perhaps  the   most 
interesting  and  most  promising  is  that  relating  to  alternating 
currents.     In  this  connection  a  few  words   concerning  the 
remarkable  experiments  of  Tesla  may  not  be  out  of  place. 

Tesla's  work  has  been  especially  with  alternating  currents 
of  very  high  frequency  and  enormously  high  potential.  In 
his  experiments  he  operates  an  induction  coil  either  with  a 
specially  constructed  alternating  dynamo  capable  of  giving 
many  thousands  of  reversals  of  current  per  second,  or  by  dis- 
ruptively  discharging  a  condenser  through  the  primary.  By 
the  latter  means  may  be  produced  a  vibration  in  the  secondary 

1  For  details  on  this  subject,  see  "  Experiments  with  Alternating  Currents  of 
High  Potential  and  High  Frequency,"  by  Tesla. 


364  ETHER   DYNAMICS. 

circuit  of  a  frequency  of  many  hundred  thousands  or  even 
millions  per  second.  The  apparatus  is  usually  enclosed  in  a 
wooden  box  and  completely  immersed  in  oil,  that  the  insula- 
tion may  be  more  nearly  perfect.  The  discharge  produced  by 
this  means  is  quite  different  from  the  series  of  sparks  pro- 
duced by  the  ordinary  induction  coil.  Herein  is  opened  to 
the  experimenter  a  field  as  yet  quite  unexplored. 

If  two  straight  wires  terminate  the  secondary  coil  and  run 
parallel  to  each  other  for  a  short  distance,  the  discharge 
appears  in  the  form  of  powerful  brushes  and  luminous 
streams  issuing  from  all  points  of  the  wires.  When  an 
ordinary  low-frequency  discharge  is  passed  through  moder- 
ately rarefied  air,  the  air  assumes  a  purplish  hue  ;  but  if  by 
some  means  the  intensity  of  the  molecular  or  atomic  disturb- 
ance be  increased,  the  gas  changes  to  a  white  color.  A  similar 
change  occurs  in  air  at  ordinary  pressure  when  agitated  by 
electric  impulses  of  the  high  frequency  .obtained  by  Tesla. 

The  chief  interest  in  investigations  along  this  line  seems  to 
lie  in  the  possibilities  they  offer  for  the  production  of  an  effi- 
cient illuminating  device.  The  present  means  of  producing 
artificial  light  is  woefully  inefficient  and  wasteful.  Who 
can  say  that  it  is  not  to  be  by  means  of  alternating  currents 
of  high  frequency  and  high  potential  that  we  shall  soon  vie 
with  the  firefly  in  economical  illumination  ? 


REVIEW   EXERCISES. 

1.  How  is  a  body  charged  by  conduction  ?     How  by  induction  ? 

2.  In  a  circuit  of  large  resistance  which  would  be  more  sensitive,  a 
long-coil  or  a  short-coil  galvanometer  ?     Why  ? 

3.  How  does   the   condition   of    a  wire  and  its  surroundings  when 
traversed  by  a  current  differ  from  that  of  a  wire  when  not  traversed  by  a 
current  ? 

4.  What  conditions  are  the  prerequisite  of  a  current  of  electricity  ? 

5.  If  a  current  be  sent  through  the  armature  of  a  dynamo,  what 
happens  ?     Why  ? 


REVIEW   EXERCISES.  365 

6.  Upon  what  conditions  does  the  strength  of  a  current  furnished  by 
a  dynamo  depend  ? 

7.  You  wish  to  make  of  an  iron  rod  an  electro-magnet  with  a  certain 
end  as  an  j^-pole.     Explain  the  method  by  a  diagram. 

8.  What  is  the  strength  of  a  current  which,  falling  15  volts,  yields 
.002  horse-power  ? 

9.  When  would  you  wind  an  electro-magnet  with  fine  wire  ? 

10.  If  the  difference  of  potential  between  the  terminals  of  an  arc 
lamp  supplied  with  a  10-ampere  current  be  50  volts,  what  is  the  power 
consumed  in  the  lamp  ? 

11.  A  difference  of  potential  of  5.5  volts  is  maintained  at  the  termi- 
nals of  a  wire  of  0.1   ohm  resistance,     (a)  What  current  flows?    (6) 
What  is  the  power  of  the  current  ? 

12.  To  which  electrode  must  an  article  to  be  electroplated  be  attached  ? 
Why? 

13.  Explain,  in  accordance  with  Ampere's  theory  of  magnetism,  the 
deflection  of  a  magnetic  needle  by  an  electric  current. 

14.  What  length  of  copper  wire  .012  inch  in  diameter  will  offer  a 
resistance  of  1  ohm  ? 

15.  What  currents  are  difficult  to  insulate  ?    Why  ? 

16.  Upon  what  does  the  E.  M.  F.  of  a  dynamo  depend  ? 

17.  (a)  How  does  a  storage  cell  differ  from  a  voltaic  cell  ?     (6)  What 
can  you  say  as  to  the  direction  of  the  current  produced  by  each  ? 

18.  Which  pole  of  an  electro-magnet  is  that  where  the  direction  of  the 
current  in  the  coil  is  anti-clockwise  ? 

19.  What  must  be  the  E.  M.  F.  of  a  generator  which  maintains  a  cur- 
rent of  5  amperes  and  works  at  the  rate  of  60  watts  ? 

20.  If  the  resistance  of  40  feet  of  wire  TJ¥  inch  in  diameter  be  4 
ohms,  what  is  the  resistance  of  80  feet  of  like  wire  |-  inch  in  diameter? 

21.  If  the  resistance  of  an  electric  lamp  be  90  ohms,  what  would  be 
the  resistance  of  10  such  lamps  connected  (a)  in  series  ?  (6)  in  multiple  ? 

22.  The  resistance  between  two  points  in  a  conductor  is  40  ohms,  but 
on  shunting  these  points  it  falls  to  10  ohms.     What  is  the  resistance  of 
the  shunt  ? 

23.  How  many  watts  are  consumed  in  a  32  candle-power  lamp  requir- 
ing an  E.  M.  F.  of  54  volts  and  a  current  of  1.75  amperes  ? 

24.  How  many  cells  in  series  each  having  an  E.  M.  F.  of  1.5  volts  and 
an  internal  resistance  of  2.5  ohms  will  produce  a  current  of  £  ampere 
through  an  external  resistance  of  10  ohms  ? 

25.  Why  is  a  battery  composed  of  cells  no  larger  than  percussion  gun 
caps  practically  as  efficient  for  sending  a  message  through  an  ocean  cable 
as  a  battery  of  an  equal  number  of  cells  as  large  as  flour  barrels  ? 


Inches 


h k 


10 


Millimeters 


Square   j 

Centimeter! 


Centimeters 


Milliliter  Cubic  Centimeter 

The  area  of  this  figure  is  a  square  decimeter. 
A  cube  of  water,  one  of  whose  sides  has  this 
area,  is  a  cubic  decimeter  or  a  liter  of  water, 
and  at  the  temperature  of  4°  C.  has  a  mass  of 
a  kilogram.  The  same  volume  of  air  at  0°  C., 
and  under  a  pressure  of  one  atmosphere,  has  a 
mass  of  1.293  grams.  The  gram  is  the  mass 
of  1  cc  of  pure  water  at  4°  C. 


Square  Inch 


ill  III  III  III  II  111  III  1 1  III  ill  ill  I  IB  I •  •  •  •  ffil flll  Hill  lill  III  ill  III  I •  ••  •  «  • 


100  Millimeters 


APPENDIX. 

00^00 

TABLES  OF  METRIC  MEASURES. 


MEASURE  OF  LENGTH. 

1  Millimeter  (mm.)  =  .001  meter  (m.)  =  .03937  inch. 
1  Centimeter  (cm.)  =  .01    meter          —  .39371  inch. 
1  Decimeter  (dm.)  =  .1      meter          =  about  4  inches. 
1  Meter  =  39.37079  inches  =  about  3  ft.  3|  in. 

1  Kilometer  (km.)  1000  meters  =  about  f  mile. 


MEASURE  OF  SURFACE. 

1  Square  millimeter  (mm.2)  =  .000001  square  meter  (m.2)  =  .0015  sq.  in. 
1  Square  centimeter  (cm.2)  =  .0001      square  meter  =  .1550  sq.  in. 

1  Square  decimeter  (dm.2)   =  .01          square  meter. 
1  Are  =  100         square  meters. 

MEASURE  OF  VOLUME. 

1  Cubic  millimeter  (mm.3)  =  .000000001  cubic  meter  (m.3). 

1  Cubic  centimeter  (cm.3  or  cc.)  =  .000001  m.3  =  .061  cu.  in. 
1  Cubic  decimeter  (dm.3)  =  .001  m.3       =  1000  cm.3. 

1  Cubic  meter  =  about  1.308  cu.  yds. 

MEASURE  OF  CAPACITY. 

1  Milliliter  (ml.)  =  .001  liter  (1.)  =  1  cc.  =  .061  cu.  in. 
1  Centiliter  (cl.)  =  .01    liter       =  10  cc. 
1  Deciliter  =  .1      liter    *  =  100  cc. 

1  Liter        =  1000  cm.2  =  61.027  cu.  in.  =  1.0567  qts. 
(liquid  measure). 


368  APPENDIX. 


MEASURE  OF  MASS  AND  WEIGHT. 

1  Milligram  (mg.)  =  .001  gram  (g.)  =  .0154  grain. 
1  Centigram  (eg.)  =  .01  gram  =  .1543  grain. 
1  Decigram  (dg.)  =  .1  gram  =  1.5432  grains. 

1  Gram  =  1.5432  grains  =  .03527  av.  oz. 

1  Kilogram  (kg.  or  k.)  =  1000  grams  =  2.2046  av.  Ibs. 

TABLE  or  EQUIVALENT  VALUES. 

1  in.     =  .0254  m.  =  2.53995  cm.  =  about  2|  cm. 
1  ft.      =  .3048  m.  =  30.48  cm.      =  about  30 J  cm. 
1  yd.    =  .9144  m.  =  about  tf.  in. 
1  mile  =  1609  m.  =  about  1.609315  km. 

1  sq.  in.   =  6.4514  cm.2. 
1  sq.  ft.    =  929.01  cm.2. 
"1  sq.  yd.  =  8361.1  cm.2  =  .83611  m.2. 

1  cu.  in.    =  16.38618  cm.3. 

1  cu.  ft.    =  28,316  cm.3. 

1  cu.  yd.  =  764,526  cm.3  =  about  .76  m.8. 

1  U.  S.  quart  =  946  cc.  =  .946  1. 

1  av.  oz.          =  28.3494  g. 

1  av.  Ib.          =  453.59  g.  =  .45359  k.  =  about  T5T  k. 

REDUCTION  OF  MEASURES  TO  AND  FROM  THE  C.  G.  S.  SYSTEM. 

1  gram  weight     =  980  dynes  (where  g.  =  980  cm.  per  sec.). 

1  av.  Ib.  weight  =  4.445  X  105  dynes          "  " 

1  k.  weight          =  980,000  dynes  "  " 

1  gram-centimeter  =  980  ergs. 

1  erg  =  1  dyne-centimeter  =  .0000001  joule  =  ^  gram-centimeter. 

1  kilogrammeter  =  98,000,000  ergs  =  7.23314  ft.  Ibs. 

1  ft.  Ib.  =  13,550,000  ergs. 

1  foot-poundal     =  421,402  ergs.1 

1  joule  =  10,000,000!  ergs. 

3300°  ft"  lbs"  Per  min'  ~  ab°llt  7'452  X  1{)9  GT&  P6r  SeC> 

75  kilogrammeters  per  sec.  =  7.35  X  109  ergs  per  sec. 
1  watt  =  1  joule  per  sec.  =  107  ergs  per  sec.  =  44.2394  ft.  Ibs.  per  min. 
1  gram-degree  =  4.17  x  107  ergs. 
1  calorie  =  4.17  X  1010  ergs.  -    ? 

to 

1  Independent  of  acceleration  of  gravity  (g.). 


APPENDIX. 


369 


PROPERTIES  OF  SOLIDS. 


Specific 
Density 
17°  C. 

Hard- 
ness. 

Expan- 
sion 
Coefficient 
Oc-100°. 

Melting 
Point. 

Specific 
Heat. 

Latent 
Heat  of 
Fusion. 

Refrac- 
tive 
Index. 

Agate 

2.6 
1.7 
2.7 
6.7 
5.7 
.8 

7 
2+ 
3 
3 
3 

1.54 
1.45 

Alum 

Aluminum  
Antimony  

.00002 
.00001 
.000007 

700° 
432° 

.21 
.05 

.08 

Arsenic 

Beech 

Bismuth 

9.8 
9 
8.3 
8.5 
1.7 

2 
3  

.000013 

266° 

.03 

13 

Boxwood 

Brass  (cast)  
"      (hard  drawn) 
Bricks 

.000019 

900°? 

.09 

.2 

Bronze  
Canada  Balsam  
Cherry    

8.8 
1.07 

.7 

3 

1.53 

Copper  

8.8 
.24 

3.5 

2.7 
2.5 
8.5 
2.5 
3.6 
19.3 
2.7 

3 

.000017 

1100° 

.09 

30 

Cork 

Diamond 

10 

8 
6 
3 

.14 

2.47 
1.58 

Emerald 

Feldspar 

.00002 
.000007 

German-silver  
Glass  (crown)  
"     (flint)  
Gold  
Granite 

400° 

.19 

1.51 
1.62 

.000012 

1050° 

.03 

Graphite 

2.3 

.20 

Ice 

.9 

1.5 

0° 

.5 

79.7 
(  Ord. 
j  Extr. 

1.31 
1.66 
1.49 

Iceland  spar 

2.7 

Iron  (cast) 

7.2 
7.7 
1  9 

6? 
4 

.000012 

1500° 

.11 

"     (wrought)  
Ivory  
Lead         

1.53 

11.3 
2.7 

2.8 

2 
3 

.000028 

326° 

.03 
.21 

5 

Marble  

Mica 

Parafifine 

.9 

55° 
1800° 

Platinum  (wire)  
Quartz 

21.4 
2.6 
2.2 
2.3 
10.4 

7 

2 
2 

.000008 

.03 

1.54 
1.54 
1.52 

Rock  salt 

800° 

.21 



Selenite  
Silver 

.000019 

1000° 

.05 

24 

Slate 

2.8 

Spermaceti  
Steel  (tempered)  
Sulphur  (native)  
Talc                

.9 
7.8 
2. 
2.6 
.9 
7.3 
7.1 

9?" 

.000013 

44° 

.08 

1.54 

£03 

115° 

.17 

9 

1 

2 
3 

Tallow      

.000019 
.00003 

40° 
232° 
360° 

....„„.... 
.09 

14 
28 

1.49 

Tin 

Zinc  ... 

370 


APPENDIX. 


PROPERTIES  OF  LIQUIDS. 


Specific 
Density. 

Coefficient 
Expan- 
sion at  0°. 

Freez- 
ing 
Point. 

Boiling 
Point 
760mm. 

Specific 
Heat. 

Refrac- 
tive 
Index. 

Acid,  nitric,  0° 

1.5 

.00111 

—  47° 

"     sulphuric,  0° 

1.84 

.00059 

330°? 

.34 

1.43 

Alcohol  (grain),  0° 

.81 

.00106 

78.2° 

.59 

1.36 

Benzine,  20°  
Carbon  dioxide,  20° 

.87 
1.37 

.00118 

4° 

80° 

.39 

1.49 

"       disulphide,  15° 

1.26 

.23 

1.64 

Ether,  0°  
Glycerine,  0° 

.73 
1.26 

.00148 
.0005 

35° 
290° 

.54 

1.35 
1.47 

Mercury,  0°  (Regnault).... 
"         15°-20°  . 

13.596 
13.558 

.00018 

—  39° 

350° 

.034 

"         (solid)   —40° 

14.3 

Milk,  0° 

1.032 

Oil  of  turpentine,  0°  
Olive  oil,  0°  

.89 
.92 

.00071 

.00080 

-10° 

160° 

.43 

1.47 
1.47 

Sea  water,  0° 

1.026 

Water,  0° 

.999 

0° 

100° 

1.00 

"      4.07°  

1.000 

1.33 

"       20° 

.998 

"       100°  

.958 

SPECIFIC  DENSITY  OF  GASES  AND  VAPORS. 
(Standard  :  Air  at  0°  C. ;  barometer,  76  cm.) 


Air 1.0000 

Ammonia 0.5367 

Carbonic  acid 1.5290 

Chlorine  3.4400 

Hydrochloric  acid 1.2540 


Hydrogen  0.0693 

Nitrogen 0.9714 

Oxygen 1.1057 

Sulphuretted  hydrogen 1.1912 

Sulphurous  acid 2.2474 


APBENDIX.  371 


YOUNG'S   MODULUS   OF   ELASTICITY. 

A  rod  of  metal  or  a  wire  may  have  its  length  increased  by  pulling. 
The  important  quantity  known  as  Young'' s  Modulus,  M,  is  the  stretching 
force  per  unit  area  of  cross  section  divided  by  the  elongation  produced  per 
unit  length.  — 

Thus,  let  a  rod  of  length  I,  and  cross  section  a,  be  stretched  by  the  force 
/  so  that  its  length  becomes  I  +  V  ;  then  the  strain  per  unit  of  length  is 

- ,  and  the  stress  is  - ;  hence,  Young's  modulus  is 


The  numerical  value  of  M  in  any  case  depends  upon  the  unit  of  force 
used  and  the  unit  employed  in  measuring  the  cross  section.  For  exam- 
ple, if  the  unit  of  force  be  the  pound,  and  if  the  cross  section  be  meas- 
ured in  square  inches,  the  value  of  E  for  iron  is  about  25,000,000.  This 
means  that  a  rod  of  iron  1  sq.  in.  in  section  will,  under  a  load  of  (say) 
10,000  Ibs.  (4.46  tons),  have  its  length  increased  ^o  Part-  If  the  rod 
be  6  ft.  long,  its  length  will  be  increased  by  fully  -^  of  an  inch. 


TABLE   OF  RESISTANCE   OF   WIRE, 

Chemically  pure,  one  meter  long,  one  millimeter  in  diameter, 
at  0°  C.   (Jenkin).     Also  relative  resistances  (Ayrton). 

Relative 

Resistances. 

Silver,  annealed 01937  ohm    .     .     .  1.000 

Copper,  annealed 02104  "      ...  1.086 

Zinc,  pressed 07244  "...  3.741 

Platinum 11660  "...  6.022 

Iron,  annealed 12510  "       ...  6.460 

Lead,  pressed 25270  "...  13.050 

German  silver                               .     .     .     .26950  "...  13.920 


372 


APPENDIX. 


TABLE    OF   TANGENTS. 


ARC. 

TANGENT. 

ABC. 

TANGENT. 

ARC. 

TANGENT. 

1 

.017 

31 

.601 

61 

1.80 

2 

.035 

32 

.625 

62 

1.88 

3 

.052 

33 

.649 

63 

1.96 

4 

.070 

34 

.675 

64 

2.05 

5 

.087 

35 

.700 

65 

2.14 

6 

.105 

36 

.727 

66 

2.25 

7 

.123 

37 

.754 

67 

2.36 

8 

.141 

38 

.781 

68 

2.48 

9 

.158 

39 

.810 

69 

2.61 

10 

.176 

40 

.839 

70 

2.75 

11 

.194 

41 

.869 

71 

2.90 

12 

.213 

42 

.900 

72 

3.08 

13 

.231 

43 

.933 

73 

3.27 

14 

.249 

44 

.966 

74 

3.49 

15 

.268 

45 

.000 

75 

3.73 

16 

.287 

46 

.036 

76 

4.01 

17 

.306 

47 

.07 

77 

4.33 

18 

.325 

48 

.11 

78 

4.70 

19 

.344 

49 

.15 

79 

5.14 

20 

.364 

50 

.19 

80 

5.67 

21 

.384 

51 

.23 

81 

6.31 

22 

.404 

52 

.28 

82 

7.12 

23 

.424 

53 

.33 

83 

8.14 

24 

.445 

54 

.38 

84 

9.51 

25 

.466 

55 

.43 

85 

11.43 

26 

.488 

56 

.48 

86 

14.30 

27 

.510 

57 

.54 

87 

19.08 

28 

.632 

58 

.60 

88 

28.64 

29 

.554 

59 

.66 

89 

57.29 

30 

.677 

60 

.73 

90 

Infinite 

APPENDIX. 


373 


VALUE  IN  MILLIMETERS  OF  BROWN  &  SHARPE  WIRE- 
GAUGE   NUMBERS. 


Number. 
1    .      .     .      ... 

Diameter 
mm. 

7.348 

Number. 
21 

Diameter 
mm. 

0  723 

2    . 

6  544 

22 

0  644 

3    . 

.    5.827 

23    .     . 

.     .     .     .     .0  573 

4    .     . 

.    5.189 

24         ... 

0  511 

5   
6   

.    4.621 
.    4.115 

25    .... 
26    . 

0.455 
.     .     .         0  405 

7   ........ 
8   

.    3.656 
.    3.264 

27    .... 

28   .... 

....    0.361 
.     .    0  321 

9   .     . 

2  906 

29 

0  286 

10    "'. 

.    2.582 

30   .... 

.     .     .         0  255 

11    ..... 

2  305 

31 

0  227 

12 

2  053 

32 

0  202 

13   

.    1.828 

33    .. 

0  180 

14    . 

.    1  628 

34 

0  160 

15   

.    1.459 

35    .... 

.     .              0  143 

16    

1.291 

36   ... 

0  127 

17    

.    1.150 

37    .... 

0  113 

18    

.    1.024 

38   . 

0  101 

19   
20   . 

.    0.912 
.    0.812 

39    .... 
40   . 

....    0.090 
.    0.080 

DEVELOPMENT   OF   PHYSICAL   SCIENCE. 

Modern  scientific  knowledge  comprises  a  very  large  body  of  facts, 
grouped  under  a  comparatively  few  comprehensive  generalizations,  and 
these  form  a  starting  point  for  further  investigations.  But  for  centuries 
scientific  study  was  confined  to  the  observation  of  the  more  obvious 
isolated  facts  only,  and  to  the  construction  of  crude,  because  purely 
speculative,  hypotheses. 

It  is  the  glory  of  the  early  investigators  that  in  apparently  unrelated 
fields  of  observation,  and  with  no  aid  from  the  conception  of  the  unity  of 
scientific  processes,  they  yet  were  able  to  formulate  certain  laws  of  the 
utmost  value  to  later  investigators.  Among  these  pioneers  was 

Archimedes  (page  118),  287-212  B.C.,  a  native  of  Syracuse,  who  was 
the  greatest  mathematician  of  his  age,  and  was  skilled  in  various  branches 
in  Natural  Philosophy.  His  principal  discovery,  that  of  the  law  of  buoy- 


374  APPENDIX. 

ancy  of  fluids  (see  §113),  is  the  foundation  of  the  science  of  specific 
gravity.  He  also  discovered  the  principle  of  the  lever,  and  the  applica- 
tion of  the  inclined  plane  in  the  Archimedean  screw. 

From  the  third  to  the  sixteenth  century,  science  made  but  little  prog- 
ress. Modern  science,  in  which  theory  is  verified  by  observation  under 
selected  conditions,  may  be  said  to  date  from 

Galileo  (page  38),  A.D.  1564-1642,  an  Italian  mathematician,  astron- 
omer, and  physicist.  He  is  credited  with  being  the  founder  of  experi- 
mental science.  The  discovery  of  the  isochronism  of  the  vibrations  of  the 
pendulum,  attributed  to  him,  made  it  possible  to  develop  a  science  of  the 
relations  of  the  three  basal  quantities,  time,  space,  and  force,  to  which 
his  demonstration  of  the  law  of  falling  bodies  (§  40)  still  further  con- 
tributed ;  while  his  invention  of  the  astronomical  telescope  (§  272)  made 
possible  modern  astronomy,  and  that  of  the  thermometer  made  possible 
the  study  of  heat. 

Sir  Isaac  Newton  (page  28),  1642-1727,  is  styled  "Prince  of 
Philosophers."  His  penetrating  mind  traced  the  principles  which  gov- 
ern the  motions  of  the  planets  in  their  orbits  and  preserve  the  order 
of  the  universe.  Not  only  did  he  formulate  the  Law  of  Gravitation 
(§  65),  but  he  enunciated  the  three  universal  laws  of  motion  (page  27), 
and  by  his  discussion  of  mass,  momentum,  inertia,  force,  etc.,  went  far 
towards  constructing  a  complete  science  of  molar  dynamics  ;  and  the 
principles  propounded  in  his  works  contain  by  implication  the  modern 
doctrine  of  energy.  In  the  field  of  optics,  he  discovered  the  principle  of 
the  different  refrangibility  of  colors  and  propounded  the  corpuscular 
theory  of  light  (§  214).  His  work  in  mathematics  was  as  profound  and 
comprehensive  as  that  in  physics.  Pope  said  of  his  vast  achievements : 

Nature  and  Nature's  Laws  lay  hid  in  Night ; 
God  said,  Let  Newton  be!  and  all  was  Light. 

Yet  at  the  close  of  life  he  declared,  "I  seem  to  have  been  only  like  a 
boy  playing  on  the  seashore,  and  diverting  myself  in  now  and  then  find- 
ing a  smoother  pebble,  a  prettier  shell  than  ordinary,  while  the  great 
ocean  of  truth  lay  all  undiscovered  before  me." 

Newton  was  followed  by  a  very  large  number  of  earnest  students  of 
nature,  some  of  whom  founded  the  science  of  chemistry,  while  others 
investigated  the  subjects  of  light,  heat,  and  electricity. 

Benjamin  Franklin  (page  278),  1706-90,  was  an  American  states- 
man and  a  scientist  of  original  powers.  He  demonstrated  the  identity 
of  lightning  with  the  electric  spark,  and  investigated  vitreous  and 


APPENDIX.  375 

resinous  electricity  (§  282).  The  former  lie  attributed  to  an  excess,  the 
latter  to  a  deficiency  of  an  hypothetical  "electric  fluid,"  and  thus  gave 
to  electrical  terminology  the  expressions  "positive"  and  "negative" 
electricity.  His  discovery  that  the  boiling  point  of  liquids  varies  with 
the  pressure  (§  150)  was  a  distinct  step  in  advance  in  the  study  of  the  three 
states  of  matter,  and  his  investigations  of  atmospheric  phenomena  fore- 
shadowed the  modern  science  of  meteorology. 

The  nineteenth  century  has  far  surpassed  all  previous  centuries  in  the 
amount  and  the  quality  of  its  contributions  to  scientific  knowledge  and 
theory.  Of  the  many  names  of  scientists  who  have  contributed  in  a 
marked  degree  to  the  advancement  of  modern  science,  we  can  mention 
only  Faraday  and  Thomson. 

Michael  Faraday  (page  330),  1791-1867:  as  a  scientific  investigator, 
he  stands  preeminent  by  his  rare  combination  of  the  speculative  and 
imaginative  power  in  originating  experiments  with  manipulative  skill 
in  conducting  them.  He  established  the  identity  of  the  forces  manifested 
in  the  phenomena  known  as  electrical,  galvanic,  and  magnetic,  and  laid 
the  foundation  of  the  science  of  electricity.  The  whole  language  of  the 
magnetic  field  and  lines  of  force  is  Faraday's.  Especially  notable  are  his 
studies  in  electrolysis,  in  electrical  induction,  and  in  electro-magnetism. 

Sir  William  Thomson  (page  306),  1824-,  was  raised  in  1892  to  the 
peerage  as  Lord  Kelvin.  In  the  scientific  world  he  is  noted  for  his 
researches  and  his  contributions  to  scientific  literature,  and  for  the 
invention  of  many  electrical  instruments  of  great  scientific  value. 

To  the  general  public  he  is  best  known  by  his  work  in  connection  with 
submarine  telegraphy  (1858-66),  while  among  scientists  he  commands 
respect  by  his  profound  and  exhaustive  study  of  molecular  motion, 
his  masterly  attempts  to  unify  the  sciences  of  light,  heat,  electricity,  and 
magnetism  under  a  general  theory  of  molecular  physics,  and  his  subtle 
speculations  in  regard  to  the  ultimate  constitution  of  matter. 

Helmholtz  wrote  of  him  as  follows  :  "  His  particular  merit,  in  my 
opinion,  consists  of  his  treatment  of  mathematical  physics.  He  has 
striven  with  great  consistency  to  purify  the  mathematical  theory  from 
hypothetical  assumptions  which  are  not  pure  expressions  of  facts.  In 
this  way  he  has  done  very  much  to  destroy  the  old  unnatural  separation 
between  the  experimental  and  mathematical  physics,  and  to  reduce  the 
latter  to  a  precise  and  pure  expression  of  the  laws  of  phenomena." 


377 


INDEX. 


[Numbers  refer  to  pages.] 


Aberration,  Chromatic,  240  ;  Spher- 
ical, 237. 

Absolute  temperature,  140;  units, 
35,  36 ;  zero,  139. 

Acceleration,  10  ;  Laws  of,  11,  38. 

Action  and  reaction,  31. 

Adhesion,  94. 

Air-pump,  114. 

Ammeter,  299. 

Ampere,  292. 

Ampere's  laws,  327. 

Ampere's  theory  of  magnetism,  327. 

Ampere-volt,  294. 

Analysis  of  light,  239. 

Astigmatism,  262. 

Atmospheric  pressure,  106. 

B 

Barometer,  109;  Fortin,  110. 
Batteries,  308. 
Beam  of  light,  209. 
Beats  in  music,  194. 
Boyle's  law,  112. 
Buoyancy,  117. 

C 

Caloric,  132. 
Calorimetry,  131. 
Candle-power,  214. 
Capillary  phenomena,  95. 
Cell,  Voltaic,  279,  306;    Storage, 
347. 


Center  of  mass,  48 ;  of  oscillation, 
62. 

Central  force,  57. 

Centrifugal  force,  58. 

Chord,  Musical,  196. 

Cohesion,  91,  94. 

Cold,  Artificial,  150. 

Color,  249-56 ;  blindness,  254. 

Colors,  Complementary,  254. 

Commutator,  340. 

Composition  of  forces,  41,  44,  45; 
of  velocities,  17. 

Compressibility,  3. 

Concord,  196. 

Conduction  of  heat,  154 ;  of  elec- 
tricity, 271. 

Conductivity,  294. 

Conjugate  foci,  233. 

Conservation  of  energy,  159. 

Convection  of  heat,  155. 

Correlation  of  energy,  159. 

Coulomb,  292. 

Couple,  Dynamical,  45. 

Critical  angle,  228. 

Curvilinear  motion,  57. 


Declination  of  needle,  321. 
Deflection  of  needle,  288. 
Densimeter,  121. 
Density,  6,  119. 
Dew-point,  153. 
Diathermancy,  263. 


378 


INDEX. 


Dielectrics,  272. 
Diffused  light,  218. 
Discord,  195,  196. 
Dispersion,  241. 
Distillation,  148. 
Divided  circuit,  307. 
Divisibility  of  matter,  2. 
Ductility,  94. 
Dynamics,  25. 
Dynamos,  336. 
Dyne,  35. 


,  203. 

Earth  a  magnet,  319. 
Ebullition,  145. 
J£cfa>,  179. 
Elasticity,  92  ;  of  gases,  112  ;  Mod- 

ulus of,  372. 
Electric  lighting,  349. 
Electrification,  268. 
Electrolysis,  286,  346. 
Electro-magnets,  288,  325. 
Electro-motive  force,  292. 
Electroscopes,  270. 
Electrotyping    and    electroplating, 

352. 
Energy,   Electrical,   294;    Kinetic 

and  potential,  68  ;   of  chemical 

separation,  69;  of  sound-waves, 

176;  Units  of,  70. 
Engine,  Steam,  162. 
Equilibrant,  42. 
Equilibrium,  41,  50. 
Erg,  71. 

Ether,  The,  206. 
Evaporation,  145. 
Expansibility,  3. 
Expansion,  Anomalous,  137  ;    Co- 

efficient of,  136  ;  factors,  136  ;  by 

heat,  135. 
Eye,  260. 


Fluidity,  7. 

.FYwids,  7,  26. 

Fluoroscope,  363. 

Foci,  Conjugate,  233. 

Focus,  Principal,  221. 

Force,  25,  27,  34;  Balanced,  41; 
Central,  57 ;  Gravitation  units 
of,  34 ;  Leverage  of,  46 ;  Measure- 
ment of,  35,  37  ;  Moment  of,  45 ; 
Resolution  of,  55;  Unbalanced, 
42. 

Forces,  Composition  of,  41,  44,  55 ; 
Equilibrium  of,  41 ;  Parallelo- 
gram of,  53. 

Formula  for  concave  mirrors,  22; 
for  lenses,  233. 

Fraunhofer's  lines,  247. 

Freezing  machines,  151. 

Fusion,  142. 


Galileo's  experiment,  38. 
Galvanometer,  298,  306,  308. 
Galvanoscope,  290. 
Gaseous  masses,  Laws  of,  140. 
Gravitation,  65. 
Gravity,  Specific,  119. 


Hardness,  93. 

Harmonic  motion,  166. 

Harmonics,  192. 

Harmony,  195. 

Heat  capacity,  132;  Consumption 
of,  150;  defined,  125;  Kinetic 
theory  of,  125 ;  Mechanical  the- 
ory of,  161 ;  of  fusion,  143 ;  of 
vaporization,  147;  Sources  of, 
126 ;  Specific,  132. 

Horse-power,  77. 


INDEX. 


379 


Hydrokinetics,  98. 
Hydrometer,  121. 
Hydrostatic  press,  100. 
Hydrostatics,  98. 
Hygrometry,  152. 


Illumination,  214. 

Images,  210,  217,  219,  222,  234. 

Impenetrability,  2. 

Inclined  plane,  85. 

Induction,  273 ;  coils,  332 ;  Electro- 
magnetic, 328;  Faraday 'slaw  of, 
330. 

Inertia,  27. 

Interference  of  ether-waves,  255 ; 
of  sound-waves,  183. 

Isogonic  curves,  321. 

J 

Joule,  294. 

Joule's  experiment,  160. 

K 

Kinematics,  8. 
Kinetics,  42. 

L 

Lamps,  Electric,  349. 

Law  of  Charles,  140;   of  gaseous 

masses,  140. 
Lenses,  231. 
Leverage,  46. 
Levers,  82. 
Light,  207 ;    Maxwell's  theory  of, 

359. 

Lightning,  277. 
Lines  of  magnetic  force,  315. 
Luminous  bodies,  208. 

M 

Machines,  78-91 ;  Efficiency  of,  82. 
Magnetic  circuit,  317  ;    field,  322 ; 


flux,  317;  poles  of  the  earth, 
320. 

Magnetism,  Ampere's  theory  of, 
327. 

Magnets,  313. 

Malleability,  94. 

Mass,  5,  37  ;  Center  of,  48. 

Matter,  Kinetic  theory  of,  138 ; 
Theory  of  the  constitution  of, 
3,  138 ;  Three  states  of,  7. 

Megohm,  294. 

Metric  system,  4. 

Microphone,  359. 

Microscope,  Compound,  257  ;  Sim- 
ple, 236. 

Mirrors,  217,  219. 

Molecule,  2. 

Moment  of  a  couple,  47  ;  of  a  force, 
45. 

Moments,  Equilibrium  of,  46. 

Momentum,  27,  73. 

Motion,  8 ;  Composition  and  reso- 
lution of,  17 ;  Curvilinear,  23, 
57;  Harmonic,  166;  Kinds  of, 
22;  Newton's  laws  of,  27,  28, 
31. 

Motor,  Electric,  343. 

Musical  instruments,  199;  scale, 
186;  sound,  186. 


N 


Nodes,  191. 
Notes,  193. 


Ohm,  293. 

Ohm's  law,  295,  296. 
Opalescence,  250. 
Optical  prisms,  231. 
Oscillation,  Center  of,  62. 
Overtones,  192. 


380 


INDEX. 


Parallelogram  of  forces,  53. 

Pascal's  principle,  101. 

Pendulum,  60-0* ;  Simple,  62. 

Phenomenon,  1. 

Phonograph,  197. 

Photometry,  214. 

Physical  measurements,  4. 

Physics,  1. 

Pitch,  Musical,  185. 

Plasticity,  92. 

Plates,  Sounding,  201. 

Pneumatics,  98. 

Polarity,  314,  324. 

Polarization,  Electrical,  282. 

Porosity,  3. 

Potential,  Electrical,  275,  206.   " 

Poundal,  36. 

Power,  76 ;  Electrical,  294. 

Pressure,  43;   of  gases  explained, 

138. 

PrevosVs  theory  of  exchanges,  •_(»({. 
Principle  of  Archimedes,  117. 
Prisms,  Optical,  231. 
Pumps,  114-16. 


Quality  of  sound,  196. 

R 

Radiant  energy,  206;   Effects   of, 

207. 
Radiation,  159,  206;  Electric,  359; 

Thermal  effects  of,  263. 
Radiography,  361. 
Railway,  Electric,  345. 
Ray,  209. 
Rays,   Infra-red   and    ultra-violet, 

248. 

Reenforcement  of  sound-waves.  180. 
Reflection  of  sound-waves,  178. 


If efraction,   224;    Cause   of,   226; 

Indices  of,  228. 
Relay,  356. 
Resistance,    Electrical,    293,    296, 

300,  303. 
Resonance,  179. 
Resonators,  181. 
Retentivity,  314. 
Rigidity,  26. 
Ruhmkor/'s  coil,  333. 

S 

Screw,  86. 

Self-induction,  332. 

Shadows,  211. 

Shunts,  307. 

Siphon,  116. 

Solenoid,  323. 

Sonometer,  190. 

Sound  and  sound-waves,  173,  190. 

£peafcm0-tubes,  177. 

Specific  density,  119;  gravity,  119  , 

heat,  132. 
Spectroscope,  243. 
Spectrum  analysis,  245. 
Spectrums,  243. 
Spherical  aberration,  237. 
Stability  of  bodies,  51 . 
Statics,  42. 
&feaw  engine,  162. 
Stereopticon,  262. 
Storage  cells,  347. 
Strain,  26. 

Strength  of  current,  291,  296. 
-Stress,  26. 


Telegraph,  354. 
Telephone,  356. 
Telescope,  259. 
Temperature,  128. 


INDEX. 


381 


Tenacity.  91. 

Tension,  43 ;  Surface,  95. 

Testa's  investigations,  363. 

Thermal  units,  132. 

Ther  mo-dynamics,  159. 

Thermo-electric  currents,  348. 

Thermometer,  128. 

Tones,  193. 

Transformer,  335. 

Transparency,  209 ;  Magnetic,  313. 


Units,  Absolute,  35, 36 ;  Physical,  4. 


Vaporization,  147. 

Variation  of  the  needle,  321. 

Velocity,  10 ;  Composition  and 
resolution  of,  17  ;  of  light-waves, 
212  ;  of  sound-waves,  175. 

Ventilation,  156. 


Vibration,  167,  169;   Sympathetic, 

184. 
Vibrations,  Complex,  192  ;  Station- 

ary, 191. 
Vibrograph,  169. 
Viscosity,  92,  95. 
Visual  angle,  216. 
Vocal  organs,  202. 
Volt,  293. 
Voltaic  arc,  350. 
Volt-ampere,  294. 
Volt-coulomb,  294. 
Volume,  5. 

W 


294. 

Wave-motion,  167-72. 
Weight,  6,  34,  36.  66. 
Wheatstone  bridge,  304. 
TF&eeZ  and  axle,  84. 
Work,  67,  71  ;  Electrical,  294. 


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